Project Delphi

A collection of small, self-contained reproductions of published models of biological form — from D'Arcy Thompson's transformations to present-day developmental and palaeobiological datasets — plus an evaluation layer (MorphoEval) that scores how faithfully each reproduction follows its source and publishes the scores as nanopublications.

Contents: 0. Discoveries & open problems — see the Problem Graph

1. Part 1 — How It Works: The 12-Step MorphoEval + Lean 4 Loop
   • The 12-Step Closed Loop (Tier A Build → Lean 4 Proofs → Tier B Dual-Agent Audit → Step 12 Remediation)
   • Worked Sample Run Walkthrough (2026-10-19-turing-morpho-loop: 38.0 → 85.5, +47.5 pts)
   • MorphoEval Scoreboard (All 14 Audited Simulations)
   • The Mathematics, Machine-Checked in Lean 4 and Queryable in RDF/SQL
   • Repository Map & Quick Start
2. Part 2 — The Simulations (17 Models of Biological Form, 1917–2026)
   • Index of All Simulations (by Year)
   • One worked example: Runions leaf venation
3. Part 3 — Data Sources, Extending the Repository & Analysis Tools

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How a body gets its form

Morphogenesis is how a living thing gets its shape, and regeneration is how it gets it back: cells divide, move and signal until a body plan appears, or reappears after a cut. The classic models of form reproduced here are geometric (Thompson's transformations, Raup's coiling shells, Vogel's golden-angle sunflower head, Runions's auxin space-colonisation leaf veins), chemical (Turing's reacting and diffusing morphogens, Meinhardt's shell pigmentation beside Wolfram's Rule 30) or physical (coral and stromatolite growth shaped by flow and light). The newer idea most of the rest turn on is that the pattern is also stored and read out bioelectrically: every cell holds a resting voltage across its membrane, neighbouring cells share it through gap junctions, and the resulting voltage map across a tissue tells it where a head, a tail or a limb belongs. Change the voltage and the form changes — block the junctions and a planarian regrows two heads. That is the experiment the Planform and Limbform databases record, hundreds of variants at a time, as formal graphs of what was cut, what was blocked and what grew back, and that the Cervera–Levin–Mafe model puts into equations. The repository turns such papers into running programs whose output is the form; MorphoEval then scores how faithfully each program follows its paper.

Fifteen flagship animated models of biological form across the century (1917–2021) — from D'Arcy Thompson's 600-point continuous fish silhouettes, Murray's vascular cube law, Turing–Kondo stripe insertion, and Raup's 3D coiled shells to Vogel's 3D sunflower phyllotaxis, Wolfram–Meinhardt Rule 30 cone snails, Runions's auxin leaf venation, Farhadifar's Drosophila wing vertex packing, and PlanformDB / Cervera–Levin–Mafé bioelectric planarian regeneration — each playing its full developmental trajectory once per loop with its remediated MorphoEval Audit score (mean 69.9 / 100, Pass N+1 audit 2026-10-26; several scores fell where earlier numbers rested on schematic GIFs or circular validation — see morphoeval/runs/2026-10-26-flagship15-loop-passN.md) and ranked scoreboard in the 16th tile. Made by docs/media/make_montage.py.

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Discoveries & open problems

What the reproductions found — and what is still open — lives in the Problem Graph (docs/problem-graph.html): every discovery, claim, and open problem with its status (solved / partial / open / refuted), sources, and scored registered predictions. For the long-form write-ups, see docs/KEY_DISCOVERIES.md and the plain-English docs/EXPLAINED_FOR_EVERYONE.md; for the verified-model index, see morphoeval/runs/ARISTOTELIAN_MORPHOSPACE_CATEGORIES.md and the Morphospace Explorer.

The Problem Graph in ~11 seconds — build-up, outcome tally, and the scored registered predictions. Click to explore the full graph, with sources per claim. Still poster: problem_graph_discovery_poster.png · Regenerate: python3 docs/media/make_problem_graph_animation.py.

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Part 1 — How It Works: The 12-Step MorphoEval + Lean 4 Loop

The 12-Step Closed Loop

From paper to reproduction to signed evaluation — the MorphoEval pipeline (animated GIF · high-res PNG · Mermaid source).

Every simulation in this repository is built and evaluated through a 12-step closed loop split into two tiers:

• Tier A — Making a reproduction (Steps 1–6):
  1. 1 Scout (👤 + 🤖): Pick a classic paper, an open empirical dataset, or a quantitative biological claim worth testing.
  2. 2 Paper (🤖): Extract the exact governing equations, algorithmic rules, and empirical reference tables from the primary literature.
  3. 3 Formal source (🤖): Vendor or cache the empirical tables and specimen photographs in datasets/<name>/ and lock every file by SHA-256 so any altered input is refused.
  4. 4 Pin the rules (🤖 + Lean 4): Formalize the paper's core mathematical invariants as machine-checked theorems in morphoeval/lean/MathOfBiology.lean (0 sorry, verified by the Lean 4 kernel in ~1 s) and test them on every record.
  5. 5 Script (🤖 builder): Write one self-contained Python program (<year>-<author>-<model>.py) that reproduces the model, decodes the formal graph, or tests the claim, complete with deterministic --self-test assertions.
  6. 6 Output & compare (tool): Render the static comparison figure (.png), growth/morphospace animation (.gif in docs/media/), and quantitative morphometrics table (.csv), placing simulated outputs directly beside segmented real specimens.
• Tier B — Auditing it & closing the remediation loop (Steps 7–12): 7. 7 Dual-agent audit (🤖🤖 assessors from different companies): Two independent LLM assessors from different providers (claude-fable-5-1 / claude-sonnet-5-5-high from Anthropic, gemini-4-argon from Google, gpt-5.6-sol from OpenAI) score the script across 7 weighted dimensions (0–100) with commit-pinned #L<a>-L<b> code loci:
  • Model-implementation fidelity (impl., weight 30): model-fidelity (20) + parameter-expressivity (10)
  • Biological/empirical validation (bio., weight 40): specimen-match (25) + morphometric-validation (15)
  • Reproducibility (repro., weight 30): source-traceability (10) + code-traceability (8) + repro-package (12)
  8. 8 Measure (measure_outputs.py): Hash rendered outputs (spec_fingerprint + artifact_sha256) and independently compute morphometric residuals against the empirical data in morphoeval/audits/<audit>.measurements.yaml.
  9. 9 Write as claims (build_morphoeval_kg.py): Compile the audit and measurements into governed Project Delphi Space RDF nanopublications (pk:Claim + pk:LLMClaimAssessment).
  10. 10 Sign & publish (sign_morphoeval.py + check_signed.mjs): Cryptographically sign every .trig nanopublication with RSA-2048 keys, mint immutable trusty URIs (https://w3id.org/np/RA…), and verify signatures via @nanopub/sign.
  11. 11 Public record (published.json + REPORT.md): Commit the signed nanopubs and SPARQL summary report under morphoeval/kg/<audit>/.
  12. 12 Remediate (👤 + 🤖 loop back to Step 5): Every defect found by the independent second assessor becomes an explicit checklist item. The builder re-works Step 5 (and Step 4 Lean proofs), regenerates Step 6 outputs, re-audits in Step 7, and signs a new set of nanopublications that point to the Pass 1 nanopubs via npx:supersedes (nothing published is ever overwritten).

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Worked Sample Run Walkthrough (38.0 → 85.5, +47.5 pts)

To see in detail how a complete 12-step run works from start to finish — including the exact CLI commands, Lean 4 formal proofs, Pass 1 defects caught by the second assessor, Pass 2 code fixes, per-step wall-clock & token telemetry, and signed npx:supersedes nanopublications — read the full sample run guides:

👉 Full Step-by-Step Sample Run Walkthrough: morphoeval/runs/2026-10-19-turing-morpho-loop.md (alongside morphoeval/runs/2026-10-18-runions-venation-loop.md and morphoeval/runs/2026-10-18-vogel-phyllotaxis-loop.md)

Walkthrough of the 12-step closed loop on 1952-turing-morpho.py (step-by-step sample run MD · animated GIF · high-res PNG), plus companion animated walkthroughs for 2005-runions-leaf-venation.py (GIF · PNG) and 1979-vogel-phyllotaxis.py (GIF · PNG).

• Sample Run 1 — Runions (2005) Leaf Venation, Murray's Law & Katifori Areole Topology (morphoeval/runs/2026-10-18-runions-venation-loop.md): 12/12 steps, 24.14 min (1,448.6 s) wall-clock, 56.0k LLM tokens, 76.1k artifact tokens, 6.4 s CPU. Pass 1 (8.00 min, 37.6k tokens) scored 40.9 / 100 after the independent second assessor (claude-sonnet-5-5-high, Anthropic) surfaced 5 defects (unsegmented specimen photos, 571 local 3-cycle triangles and 375 crossing edges, a synthetic proxy in Katifori loop nesting, circular JSON sampling in the Strahler test, and a trivial list-sum Lean theorem); Pass 2 (+16.14 min, +18.4k tokens) remediated all 5 defects and raised the score to 91.3 / 100 (+50.4 points), superseding the 10 Pass 1 nanopubs (RAr1cgMldoJ0TNph39c2kPLgtEnQrZfZMuVQ9LIQn1Zds npx:supersedes RA1d48WWn1smAInc0HnmtBRDiapTHGT77VXw_774OTjfc).
• Sample Run 3 — Bressloff et al. (2001) V1 Form Constants (morphoeval/runs/2026-10-19-bressloff-v1-loop.md): 12/12 steps, 47.7 min (2,860.5 s) wall-clock, 294.7k LLM tokens; Pass 1 scored 53.0 / 100 (primary) and 78.2 (blinded Gemini 4 Argon second assessor); Pass 2 (+25.6 min) remediated all 11 findings (exact retino-cortical map, $q^*$-derived wavenumber, surfaced fixture failures, Horton & Hoyt 1991 anchor) and re-scored blind to 62.8 / 100 (+9.8) and 79.2 — the smallest Pass 2 gain so far, because the re-score surfaced a second layer of defects (imposed gallery lattices, 11 uncounted upstream runs[] failures) that the first pass had not reached. Pass 3 (…-pass3.md: 59.4 min, 284.4k LLM tokens, commit d6f3c94) fixed all 15 of those and re-scored blind to 67.7 / 100 (+4.9) and 80.9 (panel 74.3): once presentation is honest, what is left to lose points on is the model itself (bare cubic coefficients that never stabilise rolls, a 3.1× wavelength gap against the paper), which is the signal the loop is meant to isolate. Pass 4 (…-pass4.md: 88.4 min, 485.1k LLM tokens, commit 2aac102) was the structural pass: the full Eq. 5.15 cubic coefficients (firing-rate derivative weights + quadratic feedback through the linear resolvent), the contoured/non-contoured regime derived from the exact orientation operator instead of a preset flag, roll stability over every $\theta$, a conformal retinal map that closes the torus (seam 0), and a paper-scale preset ($\lambda_c$ 2.60 mm); re-scored blind to 70.6 / 100 (+2.9) and 85.2 (+4.3; panel 77.9) — the tunnel and spiral are now selected planforms, and the second assessor crossed into the "faithful" band, while the primary's remaining deductions are a 5.4° hex-lattice distortion from $k_y$ quantisation, the $\sigma_0 \neq \tfrac12$ path being feedback-dominated everywhere the gallery lives, and the absence of any check against the paper's own coefficient curves.
• Sample Run 2 — Vogel (1979) / Douady–Couder (1992) Phyllotaxis (morphoeval/runs/2026-10-18-vogel-phyllotaxis-loop.md): 12/12 steps, 16.90 min (1,014.3 s) wall-clock, 167.0k LLM tokens, 5.6 s CPU; Pass 1 (8.7 min) scored 64.3 / 100 and Pass 2 (+8.2 min) remediated all 4 findings to 85.9 / 100 (+21.6 points; closed-loop diagram · animated GIF).
• Sample Run 4 — Turing (1952), Pearson (1993) & Kondo–Asai (1995) Reaction–Diffusion Morphogenesis (morphoeval/runs/2026-10-19-turing-morpho-loop.md): 12/12 steps, 25.50 min (1,529.7 s) wall-clock, 283.2k LLM tokens; Pass 1 (12.95 min, 169.5k tokens) scored 38.0 / 100 (25.1 on independent second assessor claude-sonnet-5-5-high, Anthropic) after surfacing 5 defects (missing Turing 1952 Sec. 8–10 linear dispersion and $N=20$ cell ring, missing Pearson 1993 Saddle-Node & Hopf curves and flawed $D_u=D_v$ trivial-state control, no 12-class phase diagram or diffusivity sweep, zero biological specimen validation, and 1 trivial Lean theorem); Pass 2 (+12.55 min, +113.7k tokens) remediated all findings and raised the consensus score to 85.5 / 100 (+47.5 points; 79.1 on claude-sonnet-5-5-high, +54.0 pts; closed-loop diagram · animated GIF).

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MorphoEval Scoreboard (All 14 Audited Simulations)

Scores on [0, 100] are uncalibrated criterion-referenced ratings, not probabilities ($s = 76$ does not mean $P(\text{faithful}) = 0.76$); when serialized into the governed Project Delphi templates (pk:LLMClaimAssessment and pk:Claim), score / 100 in pk:hasScore and overall / 100 in pk:weightOfEvidence are unit-interval rescalings for template conformance. Where a dimension is structurally non-applicable (not_applicable), substituting baseline 50 shrinks scores linearly toward 50 ($\bar{s}{\text{pad}} = (1-\alpha)\bar{s}{\text{app}} + 50\alpha$); the table therefore reports both the weight-renormalised applicable-only mean (app.) and the baseline-50 padded score (pad.), plus the second-assessor score (gemini-4-argon, Google, for the 10 scripts in the 2026-10-17 pass) and two-assessor panel mean:

simulation	checkpoint	primary assessor	impl. (30)	bio. (40)	repro. (30)	primary app. / pad.	2nd assessor (gemini-4-argon) app. / pad.	panel mean pad.
Runions leaf venation (2005-runions-leaf-venation.py) (sample run)	365a3cd, audit 2026-10-18-venation-v2 (was 40.9)	Gemini 4 Argon, with Claude Sonnet 5.5 (Anthropic) as second assessor inside the audit	90.7	89.8	93.9	91.3 / 91.3	— (second assessor is in the primary audit)	—
Wolfram / Meinhardt Conus textile Rule 30 (1984-wolfram-conus-textile-rule30.py)	fb234bc, audit 2026-10-18-conus	Gemini 4 Argon	87.7	85.5	89.3	87.3 / 87.3	50.5 / 50.5 (claude-fable-5-1, Anthropic, blinded, same checkpoint; impl. 47.3, bio. 38.8, repro. 69.2)	68.9
Vogel / Douady–Couder golden-angle phyllotaxis (1979-vogel-phyllotaxis.py) (sample run)	c89d18d, audit 2026-10-18-phyllotaxis-v2 (was 64.3)	Gemini 4 Argon, with Claude Sonnet 5.5 (Anthropic) as second assessor inside the audit	84.7	84.8	88.7	85.9 / 85.9	— (second assessor is in the primary audit)	—
Turing / Pearson / Kondo–Asai reaction–diffusion (1952-turing-morpho.py) (sample run)	b9976f8, audit 2026-10-19-turing-audit-v2 (was 38.0 in Pass 1; 52.7 at f3fe478)	Gemini 4 Argon, with Claude Sonnet 5.5 (Anthropic) as second assessor inside the audit (79.1; was 25.1 in Pass 1)	88.3	79.4	90.3	85.5 / 85.5	79.1 / 79.1 (claude-sonnet-5-5-high, Pass 2; was 25.1 in Pass 1)	85.5
Hoffmann–Donoughe wing venation (2018-hoffmann-wing-venation.py)	f3fe478, audit 2026-10-13	Claude Fable 5.1	81.7	80.0	71.3	77.8 / 77.8	81.3 / 81.3	79.5
Thompson Scarus → Pomacanthus on real landmarks and outlines (thompson/1917-thompson-scarus-pomacanthus.py)	232e8f8, audit 2026-10-17-thompson (re-score of 2026-10-16: 70.2)	Claude Fable 5.1	70.3	77.3	82.0	76.6 / 76.6	90.8 / 90.8	83.7
Odonata wing cells, fossil vs extant (2026-eshghi-odonata-wing-cells.py)	fbbcaf6, audit 2026-10-14-odonata	Claude Fable 5.1	63.3 (70.0 app.)	85.0	78.0	78.9 / 76.0	91.4 / 87.3	81.7
Limbform limb morphologies (2014-lobo-limbform-morphology.py)	747c57f, audit 2026-10-14-limbform	Claude Fable 5.1	81.7	61.3	74.3	71.3 / 71.3	83.6 / 83.6	77.5
WormGUIDES C. elegans embryo atlas + connectome (2015-santella-wormguides-celegans.py)	f39a409, audit 2026-10-16-celegans (re-score of 2026-10-15: 67.7)	Claude Fable 5.1	70.0 (80.0 app.)	64.4	78.0	72.4 / 70.2	81.9 / 78.7	74.4
Planform planarian morphology (2013-lobo-planform-morphology.py)	161f269, audit 2026-10-14	Claude Fable 5.1	81.7	55.0	66.7	66.5 / 66.5	76.5 / 76.5	71.5
Raup shell coiling (create_raup_animations.py)	ba6fd20, audit 2026-10-17-raup (re-score of 2026-10-13: 37.3)	Claude Fable 5.1	76.7	45.0	77.0	64.1 / 64.1	79.3 / 79.3	71.7
Bressloff V1 form constants (2001-bressloff-v1-form-constants.py) (sample run)	2aac102, audit 2026-10-19-bressloff-v4 (was 67.7 at d6f3c94, 62.8 at 9b18c52, 53.0 at 68c4a1a)	Claude Fable 5.1	70.0	63.0	81.3	70.6 / 70.6	85.2 / 85.2 (same checkpoint, blinded; was 80.9, 79.2, 78.2)	77.9
Cervera–Levin–Mafe bioelectric synthesis (2021-Cervera–Levin–Mafe.py)	a0d6848, audit 2026-10-17-cervera-v2 (was 44.9 at e71ca55)	GPT‑5.6 Sol (OpenAI)	49.3	44.3	76.9	55.6 / 55.6	60.7 / 60.7	58.1
Chindapol coral flow (2013-chindapol-coral-flow.py)	f3fe478, audit 2026-10-13	Claude Fable 5.1	53.3	43.8	70.0	55.5 / 55.5	56.0 / 56.0	55.7
Planform animation (1900-planformDB_parser.py), superseded	f3fe478, audit 2026-10-13	Claude Fable 5.1	9.3	2.5	36.3	14.7 / 14.7	—	—
Petroff stromatolite (2010-petroff-stromatolite.py), Kahng coral (2024-kahng-coral-geometry.py), Zhang sorting morphogenesis (sorting-morphogenesis/), Thompson demo (thompson/1917-thompson.py)	—	—	—	—	—	—	—	unevaluated

Across all 10 active evaluated scripts in the dual-agent pass (2026-10-17-blinded-sample-audit.yaml, gemini-4-argon, Google), rank-order agreement with the primary assessors (claude-fable-5-1, Anthropic on 9 scripts; gpt-5.6-sol, OpenAI on 2021-Cervera–Levin–Mafe.py) is strong (Spearman $\rho = 0.891$, Kendall $\tau = 0.778$, Pearson $r = 0.920$ on padded scores; $\rho = 0.903$ on applicable-only scores; and exact $\rho = 1.00$, $\tau = 1.00$ on the initial 5-script strictly blinded subset; dimension-level $\rho = 0.796$, $r = 0.813$ across all 70 dimension pairs, mean absolute difference $10.4$ points), while the independent passes surfaced concrete defects the builder had missed (including a 65-character SHA-256 typo in 2014-lobo-limbform-morphology.py).

201 nanopubs are on the production network, of which 101 are the current heads of their primary version chains (46 from 2026-10-13, 9 from the 2026-10-14 planarian re-score, 9 from the 2026-10-14 Odonata audit, 10 from the Limbform audit, 9 from the 2026-10-16 C. elegans re-score, 9 from the 2026-10-17 Thompson re-score, 9 from the 2026-10-17 Raup re-score, 9 from the 2026-10-17 Cervera–Levin–Mafe re-score, which supersedes the 9 of the first Cervera audit the same day — both by OpenAI's GPT‑5.6 Sol —, 10 from the 2026-10-18 Conus textile audit, and 54 conformant re-issues of 2026-10-16 that npx:supersedes the pre-template versions). Signed and verified (check_signed.mjs) but not yet published: the 80 second-assessor nanopubs in morphoeval/kg/2026-10-17-blinded-sample-audit/signed/, the 20 phyllotaxis nanopubs (v1 and the v2 set that supersedes it) in morphoeval/kg/2026-10-18-phyllotaxis-audit*/signed/, the 20 leaf-venation nanopubs (v1 and the v2 set that supersedes it) in morphoeval/kg/2026-10-18-venation-audit*/signed/, the 8 blinded second-assessor nanopubs for Conus textile in morphoeval/kg/2026-10-19-conus-second-assessor-audit/signed/, and the 72 Bressloff V1 nanopubs (primary v1–v4, 10 each; blinded second assessor v1–v4, 8 each) in morphoeval/kg/2026-10-19-bressloff-*audit*/signed/. Full workflow, tooling notes and the rubric text: morphoeval/README.md.

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The Mathematics, Machine-Checked in Lean 4 and Queryable in RDF/SQL

The audits record that a script follows its paper; they do not say what the paper's mathematics is in a form a machine can check or a query can reach. morphoeval/math_kg.py and morphoeval/lean/MathOfBiology.lean add that layer. For every evaluated model the governing laws are written three times — as the formula a biologist would recognise, as a Lean 4 definition with a theorem about it that the Lean kernel checks (0 sorry), and as RDF that joins the laws to the claims, the scores, the measured numbers and the commit-pinned lines of code (morphoeval/kg/math_of_biology.ttl, 16 models, 25 verified laws, 152 measurements, 4,074 triples):

system (sim_id)	law	Lean theorem
runions-leaf-venation	Murray r^γ conserved root → tips over any binary tree VeinTree	murray_1926_tree_conservation
	Runions 2005 Toussaint RNG lune test ⇔ its definition and symmetric	runions_2005_rng_lune_iff, runions_2005_rng_lune_symmetric
	Katifori 2012 Euler–Poincaré areole count (tree = 0, anastomosis +1, deletion −1)	katifori_2012_tree_zero_cycles, …_anastomosis_adds_cycle, …_edge_deletion_merges_areoles
wolfram-conus-textile-rule30	Rule 30 Boolean form ≡ GF(2) normal form	rule30_anf_equiv
	Jen 1990 left-bijective inverse; diagonal barrier shielding; 2-Sheet Quadrant PDE backward bijection	jen_1990_left_bijective, jen_1990_barrier_shielding, rule30_quadrant_pde_backward_bijective
	Oliva–Conus 10-wall source, Left-Cone 1-run profile (a=3), $D_2(t)$ linearization, 9-Row Horizon Sandwich ($k_r$), & 4-Line Inward Wavefront / Two-Band Tunneling (Theorems 44–47)	rule30_oliva_conus_10_right_wall_source, rule30_period_pi_defect_d2_linear, rule30_horizon_idempotent_shift_and_vacuum, rule30_inward_defect_wavefront_step, rule30_band1_and_band2_1run_defect_tunneling_step
	Meinhardt–Klingler activator reaction is quiescent at a = 0; Ermentrout–Oster neural gate ≡ Rule 30	meinhardt_basal_quiescence, ermentrout_oster_neural_gate_eq_rule30
vogel-phyllotaxis	Vogel r² = c²n adds constant annulus area; Fibonacci cascade	vogel_constant_annulus_area, vogel_fibonacci_parastichy_cascade
	Douady–Couder pair kernel symmetric in distance	douady_couder_kernel_symmetric
	rim dislocation can only lower a parastichy count	swinton_rim_dislocation_nonincreasing
raup-shell-coiling	whorl radius multiplies by W each whorl	raup_whorl_expansion_recovery
	T recovered from Δz/Δr	raup_translation_rate_recovery
thompson-scarus-pomacanthus	TPS kernel r² ln r² vanishes at a landmark	tps_kernel_zero_at_origin
	a unit shear is area-preserving (det = 1)	thompson_unit_shear_area_preserving
turing-gray-scott	(u, v) = (1, 0) is a homogeneous equilibrium	gray_scott_homogeneous_equilibrium
	Equal diffusion (D_X = D_Y) cannot destabilize a stable homogeneous state at any k² ≥ 0	turing_equal_diffusion_no_instability
	Differential diffusion (D_Y / D_X > d_c = 3.9271) drives Fourier determinant det(J_k) < 0	turing_differential_diffusion_instability
	Pearson Saddle-Node discriminant Δ_SN = F − 4(F+k)² = 0 & Hopf steady-state trace tr(J₀) = k − V² = 0	pearson_saddle_node_discriminant
cervera-levin-mafe	gap-junction current vanishes at equipotential	cervera_equipotential_zero_current
	Bell–Boltzmann conductance symmetric in (i, j)	cervera_bell_boltzmann_symmetric
planform-morphology-animation	wild-type AP length from the four region radii = 560	lobo_2013_wildtype_dimensions
lobo-limbform-morphology	a three-segment limb tree has three segments	lobo_2014_three_segment_axis
santella-wormguides-celegans	nuclear-position interpolation hits both endpoints	sulston_nuclear_lerp_endpoints
hoffmann-wing-venation	shoelace edge term is antisymmetric	hoffmann_shoelace_antisymmetric
eshghi-odonata-wing-cells	isotropic second moments give zero elongation	eshghi_isotropic_zero_elongation
chindapol-coral-flow	Péclet numerator vanishes at zero flow	chindapol_zero_flow_diffusive
bressloff-v1-form-constants	retino-cortical pullback: k_y = 0 → rings (tunnel), k_x = 0 → rays (funnel), else log-spiral (Ermentrout & Cowan 1979)	ermentrout_cowan_tunnel_rings, ermentrout_cowan_funnel_rays, ermentrout_cowan_log_spiral
	cubic amplitude equation: roll fixed point, transverse growth (γ₀ − 2γ₃(θ))A, roll stable ⇔ γ₀ < 2γ₃(θ); Fig. 38 instance unstable by decide	bressloff_roll_fixed_point, bressloff_roll_transverse_growth, bressloff_roll_stable_iff, bressloff_fig38_roll_unstable
	Rule 2011 Floquet multipliers: +1 returns every period, −1 returns every second period	rule_2011_harmonic_returns_each_period, rule_2011_period_doubling_even_odd

lean morphoeval/lean/MathOfBiology.lean                 # kernel-check all 25 theorems (exit 0, 0 sorry)
python3 morphoeval/math_kg.py --preset equations        # SPARQL table: organism, formula, Lean theorem, verified?
python3 morphoeval/math_kg.py --sim runions-leaf-venation # one system's card: scores, DOIs, Lean proofs, measurements
python3 morphoeval/math_kg.py --preset exact-matches    # measurements within 1.5 % of their published reference

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Repository Map & Quick Start

Each script is run directly (python3 <script>.py); rendered outputs (PNG/GIF) are written to the working directory and are git-ignored. Setup: python3 -m venv venv && source venv/bin/activate && pip install -r requirements.txt (lower bounds; requirements.lock.txt pins the exact audit environment — Python 3.14.7, numpy 2.5.4, scipy 1.16.3, matplotlib 3.10.7, scikit-image 0.26.0).

path	what it is
<year>-<author>-<model>.py (root), thompson/, sorting-morphogenesis/	one self-contained script per paper: it reproduces the paper's model, decodes the authors' formal encoding, or tests a published claim; then draws, measures and checks itself (--self-test where present)
datasets/<name>/	the formal source for each script: vendored tables and fixtures, SHA-256 pins for files that are fetched rather than vendored, a README.md with sources and licences, and paper_citations.bib
.<name>_cache/ (git-ignored)	downloads the scripts make on first run (databases, atlases, photographs, scans), each verified against a pin recorded in the script or in datasets/
docs/media/	downsized GIF/PNG of every reproduction for this README, the montage, the pipeline diagram; docs/media/README.md records how each was made
morphoeval/	the audit layer: rubric, audit YAMLs, output measurement, nanopub builder/signer/verifier, per-audit knowledge graphs (kg/), worked sample loop runs (runs/), and the Lean-checked "math of biology" graph (lean/MathOfBiology.lean, math_kg.py)
nanopubs/	the older Planform/wave nanopublication toolchain (separate from MorphoEval's signer)
wave-vector-analysis/	the Ca²⁺ wave imaging pipeline and its analysis docs (independent of the reproductions)
CITATION.cff, .zenodo.json, LICENSE (MIT)	how to cite; Zenodo deposit metadata for the MorphoEval report

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Part 2 — The Simulations (17 Models of Biological Form, 1917–2026)

Index of All Simulations (by Year)

year	model	script	MorphoEval (primary / 2nd assessor)
1917	Thompson, transformations: Scarus → Pomacanthus on real landmarks and outlines	thompson/1917-thompson-scarus-pomacanthus.py	76.6 / 90.8
1917	Thompson, transformations on a real fish	thompson/1917-thompson.py	—
1952	Turing (1952), Pearson (1993) & Kondo–Asai (1995) reaction–diffusion morphogenesis (sample 12-step run)	1952-turing-morpho.py	85.5 (v2; v1 38.0) / 79.1 (claude-sonnet-5-5-high)
1966	Raup, shell coiling	1966-raup.py, create_raup_animations.py	64.1 / 79.3
1979 / 1992	Vogel / Douady & Couder, golden-angle phyllotaxis on real Helianthus capitula (sample 12-step run)	1979-vogel-phyllotaxis.py	85.9 (v2; v1 64.3) / dual-assessed within the audit
1984 / 1987	Wolfram / Meinhardt & Klingler, Conus textile shell pigmentation & Rule 30	1984-wolfram-conus-textile-rule30.py	87.3 / 50.5
2001	Bressloff et al., V1 Euclidean symmetry-breaking & retino-cortical form constants (sample 12-step run)	2001-bressloff-v1-form-constants.py	70.6 (v4; v3 67.7, v2 62.8, v1 53.0) / 85.2
2005	Runions et al., auxin space-colonisation leaf venation, Murray's law and areole loop topology (sample 12-step run)	2005-runions-leaf-venation.py	91.3 (v2; v1 40.9) / dual-assessed within the audit
2010	Petroff et al., conical stromatolites	2010-petroff-stromatolite.py	unevaluated
2013	Chindapol et al., flow-driven coral growth	2013-chindapol-coral-flow.py	55.5 / 56.0
2013	Lobo, Malone & Levin, Planform planarian morphologies	2013-lobo-planform-morphology.py, 1900-planformDB_parser.py	66.5 / 76.5
2014	Lobo et al., Limbform limb morphologies (salamander, frog, crustacean, insect, arachnid)	2014-lobo-limbform-morphology.py	71.3 / 83.6
2015	Santella et al., WormGUIDES C. elegans embryo atlas + OpenWorm connectome	2015-santella-wormguides-celegans.py	70.2 / 78.7
2018	Hoffmann et al., insect wing venation	2018-hoffmann-wing-venation.py	77.8 / 81.3
2021	Cervera, Levin & Mafe, bioelectric morphogen antagonism	2021-Cervera–Levin–Mafe.py, evidence layer planform_bioelectric.py	55.6 / 60.7
2024	Kahng et al., coral colony geometry	2024-kahng-coral-geometry.py	unevaluated
2025	Zhang, Goldstein & Levin, autonomous cell-view sorting morphogenesis, space-time kymographs & chimeric arrays	sorting-morphogenesis/, validate_kymograph_and_paper.py	94.1 (v2)
2026	Eshghi et al., fossil vs living Odonata wing cells	2026-eshghi-odonata-wing-cells.py	76.0 / 87.3

One worked example

Only one detailed walkthrough is kept here — the best-scoring audited reproduction (91.3/100) — as a template for what every entry in the index above contains. The other 16 are catalogued in that index (script, year, MorphoEval score); each script is self-contained with its own --self-test, references, and data provenance (see Part 3), and their findings are tracked in the Problem Graph.

models/2005-runions-leaf-venation.py

Runions et al.'s (2005) auxin space-colonisation model of leaf venation, paired with Murray's (1926) minimum-work vascular power law, Price, Knox & Brodribb's (2013) Horton–Strahler transition across 349 cleared leaves (1,514,771 vein junctions), and Katifori & Magnasco's (2012) hierarchical loop-nesting metric on real and simulated leaf networks:

1. Open (dendritic, Ginkgo biloba) vs. closed (reticulate dicot) space colonisation (Runions et al. 2005, Eqs. 1–3, Table 1): In open venation (load_table1_regime("14")), each auxin source $s$ activates only its nearest vein node $v$ within perception radius $b_d$, producing an acyclic dichotomous tree ($V = 735, E = 734, L = E - V + 1 = 0$). In closed venation (load_table1_regime("15") and "10"), each source $s$ activates its Relative Neighborhood Graph (RNG) candidate set $U(s)$ — all vein nodes within $b_d$ not shadowed inside the open Toussaint lune $|s-w| < |s-v| \land |v-w| < |s-v|$ — and maintains a persistent tagged set $V(s)$ until the converging vein tips meet at $s$ (with genealogical hop exclusion tree_hop_distance >= 4 and exact planar segment-intersection rejection segments_properly_intersect), producing a planar loopy network ($V = 1,099, E = 1,507$, $L = 409$ cycles, 358 enclosed interior dual areoles, 0 crossing edges).
2. Murray's (1926) vascular power law & Price et al.'s (2013) Horton–Strahler transition: Bottom-up pipe-model accumulation $r_{\text{parent}}^\gamma = \sum_{c} r_c^\gamma$ (compute_murray_radii, residual $0.00 \times 10^0$), plus an 8-order multiscale vascular tree (build_and_measure_multiscale_strahler_tree, $2,175$ nodes, $252$ binary bifurcations) whose measured daughter-to-parent ratios $\alpha_3 = (r_1^3+r_2^3)/r_p^3$ and $\alpha_2 = (r_1^2+r_2^2)/r_p^2$ reproduce Price et al.'s (2013) empirical transition from Murray's cube law ($\gamma = 3$ in minor orders 1–2, $\alpha_3 = 0.961$ vs empirical $0.946$) to area-preserving branching ($\gamma = 2$ in major orders 5–6, $\alpha_2 = 0.996$ vs empirical $0.990$; Pearson $r = 0.9679$, $MAE = 0.0208$).
3. Pixel segmentation & planar dual areole nesting on empirical specimens (segment_empirical_specimens, compute_planar_areole_nesting_from_raster): Both vendored photographs in datasets/venation/ are segmented directly from pixels — extracting 168 enclosed planar areoles ($CV = 1.6626$) and Katifori loop-nesting index $i_u = 0.6134$ from the cleared dicot vein skeleton (reticulate_vein_skeleton_specimen.jpg) alongside 358 enclosed planar areoles and $i_u = 0.4462$ on the simulated closed network (vs. $i_u = 0.2512$ on a uniform grid control, $\Delta i_u = +0.1950$), and 1,651,010 lamina pixels with parallel dichotomous ridge density $0.4383$ ($L = 0$) on the Ginkgo biloba leaf (ginkgo_open_venation_specimen.jpg).
4. Machine-checked Lean 4 theorems: Three governing laws — inductive Murray conservation over VeinTree (murray_1926_tree_conservation), Toussaint RNG lune equivalence and symmetry (runions_2005_rng_lune_iff, runions_2005_rng_lune_symmetric), and Euler–Poincaré areole loop invariants (katifori_2012_tree_zero_cycles, katifori_2012_anastomosis_adds_cycle, katifori_2012_edge_deletion_merges_areoles) — are proved with 0 sorry in Section 13 of morphoeval/lean/MathOfBiology.lean.

python3 models/2005-runions-leaf-venation.py --self-test     # 7 deterministic mathematical, topological & specimen self-tests (<4 s)
python3 models/2005-runions-leaf-venation.py                 # self-tests + runions_leaf_venation_comparison.png, docs/media/runions_leaf_venation_growth.gif, runions_leaf_venation_metrics.csv

What you see: left, the reticulate vein network growing from the petiole into the blade step by step as veins in each auxin source's Relative Neighborhood $U(s)$ advance and anastomose into closed planar areole loops ($V = 1,099$, $L = 409$ loops, $358$ enclosed interior areoles, pipe width $\propto r_e$ under Murray's cube law $\gamma = 3$); right, the simultaneous build-up of vein segments and closed areole loops over developmental time.

MorphoEval audit 2026-10-18-venation-audit-v2 at commit 365a3cd: 91.3 (model-fidelity 92, specimen-match 89, parameter-expressivity 88, morphometric-validation 91, source-traceability 95, code-traceability 94, repro-package 93; impl. 90.7, bio. 89.8, repro. 93.9), superseding the Pass 1 audit of the same run (40.9). Full step-by-step sample run walkthrough: morphoeval/runs/2026-10-18-runions-venation-loop.md (closed-loop diagram · animated GIF). In Pass 1 (8.0 min, 37.6k tokens), the independent second assessor (claude-sonnet-5-5-high, Anthropic) caught five concrete defects — unsegmented specimen photos, 571 degenerate 3-cycle triangles and 375 crossing edges from proximity-only fusion, a synthetic proxy in the Katifori nesting metric, circular JSON sampling in the Strahler test, and a trivial list-sum Lean theorem — holding the v1 score to 40.9; all five were remediated in Pass 2 (+16.1 min, +18.4k tokens, +50.4 points), and the 10 signed v2 nanopubs (RAr1cgMldoJ0TNph39c2kPLgtEnQrZfZMuVQ9LIQn1Zds) supersede the 10 v1 nanopubs via npx:supersedes. Data and provenance: datasets/venation/.

References:

• Runions A, Fuhrer M, Lane B, Federl P, Rolland-Lagan A-G, Prusinkiewicz P (2005). Modeling and visualization of leaf venation patterns. ACM Trans. Graph. 24(3):702–711. DOI
• Murray CD (1926). The physiological principle of minimum work. I. PNAS 12(3):207–214. DOI
• Price CA, Knox S-JC, Brodribb TJ (2013). The influence of branch order on optimal leaf vein geometries: Murray's law and area preserving branching. PLoS ONE 8(12):e85420. DOI
• Katifori E, Magnasco MO (2012). Quantifying loopy network architectures. PLoS ONE 7(6):e37994. DOI; Ronellenfitsch H, Lasser J, Daly DC, Katifori E (2015). PLoS Comput. Biol. 11(12):e1004680. DOI

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Part 3 — Data Sources, Extending the Repository & Analysis Tools

Data sources

Every script's inputs are either vendored in datasets/<name>/ or fetched on first run into a git-ignored .<name>_cache/, and in both cases pinned by SHA-256 so a changed file is refused. Nothing is hand-copied from a figure without saying so, and no proprietary or unlicensed file is in the repository. The table is the complete list as of 2026-10-19; each folder's README.md has the exact file names, sizes, hashes, query URLs and retrieval dates.

folder	used by	what the source is	how it is obtained	licence
datasets/thompson/	thompson/1917-thompson-scarus-pomacanthus.py, thompson/1917-thompson.py	17 lateral landmarks for 791 Indo-Pacific shore-fish species (Claverie & Wainwright 2014 via Friedman et al. 2019, Dryad 10.5061/dryad.fn457gr); page 749 of the 1917 On Growth and Form as the Internet Archive JPEG-2000 leaf; photographs of Scarus ghobban (Huet/IFREMER) and Pomacanthus semicirculatus (Levy) from Wikimedia Commons	CSV vendored (Dryad sits behind a browser challenge); scan and photographs fetched into .thompson_cache/, pinned	CC0; public domain; CC BY 4.0 / CC BY 2.0
datasets/odonata/	2026-eshghi-odonata-wing-cells.py	Eshghi, Buesch & Gorb 2026 Tables S1–S3 (463 wings) with GBIF families and Paleobiology Database ages added; 22 fossil taxa's PBDB age records; 1762 PBDB Odonatoptera occurrences; the 69 fossil venation drawings (Zenodo 10.5281/zenodo.19899648, ~90 MB) and Hoffmann et al.'s segmented North American wings (10 MB)	tables vendored with provenance lines (GBIF/PBDB queried 2026-10-14); the two archives fetched into .wing_cache/odonata/, pinned; --zenodo-zip / --hoffmann-tar accept local copies	CC BY 4.0 (Zenodo, PBDB); GBIF API
(no folder) .wing_cache/	2018-hoffmann-wing-venation.py	one segmented hindwing of Arigomphus villosipes from hoffmannjordan/insect-wing-venation-patterns	fetched into .wing_cache/ on first run	authors' repository
datasets/planform/	2013-lobo-planform-morphology.py, 1900-planformDB_parser.py, planform_bioelectric.py, 2021-Cervera–Levin–Mafe.py	PlanformDB 2.5.0 (Lobo, Malone & Levin 2013; 372 planarian morphologies as labelled graphs); derived fixtures: the nine bioelectric experiment series (planform_bioelectric_series_v1.json, with five damaged negatives), canonical silhouettes, and the 14 Oviedo-2010 result sets, planarian circuit traces and literature targets vendored from MesmerPrism/rusty-matter; renderer-neutral 2D exports (planform_implicit_slice_2d.json, cervera_field_overlay_2d.json)	the .edb is not vendored (it ships with Planform from the Lobo lab; PLANFORM_DB_PATH); its SHA-256 and size are in planformDB.sha256 and every consumer checks them (--strict-db / pinned-only extraction); fixtures vendored	Lobo Lab notice (research/educational use with citation; reproduced in the fixtures); rusty-matter MIT OR Apache-2.0
(no folder) .limbform_cache/	2014-lobo-limbform-morphology.py	LimbformDB 2.1.0 (Lobo et al. 2014; 565 limb morphologies, SQLite, 897,024 bytes)	--download fetches it from the Lobo lab, pinned by SHA-256 in the script	Lobo Lab notice
datasets/celegans/	2015-santella-wormguides-celegans.py	WormGUIDES atlas (Santella et al. 2015): nuclear positions, diameters and lineage names for 360 frames of diSPIM series DISPIM_061416 plus cell and eggshell meshes, from a pinned commit of zhirongbaolab/WormGUIDES; the OpenWorm c302 connectome edge list (Cook et al. 2019) from a pinned commit of openworm/c302	nothing vendored; --download fetches ~430 files into .celegans_cache/ and checks them against pinned_inputs.sha256	GPL-3.0 (WormGUIDES); MIT (c302)
datasets/raup/	1966-raup.py, create_raup_animations.py	Raup's parameter definitions as restated with equations by Noshita 2014 and Okabe & Yoshimura 2017 (the 2025 extraction, written without the paper, is kept as a log with a notice); six illustrative parameter sets; paper-figure comparison stills; an exported SurfaceMesh3D bundle of the rendered shells	all vendored; there is no external dataset — the open item is to pin the definitions to Raup 1966 itself	—
datasets/conus/	1984-wolfram-conus-textile-rule30.py	two Conus textile photographs from Wikimedia Commons (James St. John / OSU; Richard Ling); the reference fixture derived from them (specimen silhouette, dorsal white-tent chord statistics) and the first 128 bits of OEIS A051023	fixture vendored; photographs fetched by --download into .conus_cache/, pinned; the script runs offline on the fixture	CC BY 2.0; public domain
datasets/phyllotaxis/	1979-vogel-phyllotaxis.py	Swinton, Ochu & MSI Turing's Sunflower Consortium 2016 Tables 1–4 (768 parastichy counts, 368 pairs, 657 capitula; Dryad 10.5061/dryad.f9k77) with Schoute 1938 and Weisse 1897; Vogel / Douady–Couder equations; two Helianthus annuus capitulum photographs from Wikimedia Commons	all vendored (photographs 399 kB and 63 kB), SHA-256 checked by --self-test	CC BY 4.0 (tables/equations as transcribed); CC BY-SA 2.0 / 3.0 (photographs)
datasets/venation/	2005-runions-leaf-venation.py	Runions et al. 2005 Table 1 (15 venation regimes); Price, Knox & Brodribb 2013 Horton–Strahler scaling over 349 cleared leaves; Katifori & Magnasco 2012 / Ronellenfitsch et al. 2015 loop-nesting benchmarks; a Ginkgo biloba leaf and a dicot vein skeleton from Wikimedia Commons	all vendored, SHA-256 checked by --self-test	CC BY-SA 3.0 (photographs)
datasets/bressloff/	2001-bressloff-v1-form-constants.py	calibration reports (Bressloff et al. 2001/2002 marginal-stability scans and planforms; Rule et al. 2011 Floquet tongues) from a pinned commit of MesmerPrism/bressloff-v1-form-constants (after karacsm/V1-sim)	vendored, SHA-256 pinned	MIT
(no folder) .cervera_cache/	2021-Cervera–Levin–Mafe.py	a dorsal photograph of Schmidtea mediterranea (Stevenson & Beane 2010, PLoS ONE, via Wikimedia Commons) whose silhouette the territories are drawn on and measured against	fetched on first run, SHA-256 pinned in the script; falls back to an ellipse and says so	CC BY 2.5
sorting-morphogenesis/catalog.json	sorting-morphogenesis/	the authors' code, Zhangtaining/cell_research at commit 1fd2bd59, read to settle rule semantics; a 4-tier claim-boundary catalogue of what the paper reports vs what the replication reconstructs	nothing copied; catalogue vendored	—
datasets/frog_embryo_data_processed/	wave-vector-analysis/	per-embryo segmentation masks (*_mask.npz), one folder per imaging zoom, for the Ca²⁺ wave detection summary	masks vendored; the raw GCaMP TIFF stacks they were made from are not in the repository	lab data

Scripts with no external data (1952-turing-morpho.py, 2010-petroff-stromatolite.py, 2013-chindapol-coral-flow.py, 2024-kahng-coral-geometry.py) run from the papers' equations alone, and the Conus script builds its own Raup shell mesh rather than reading datasets/raup/. Live services are used only at build time and their results vendored with the query and date: GBIF species match and the Paleobiology Database (Odonata families and ages) and Nanopub Query (resolving the heads of version chains before superseding). Two instances where the data did not match its source are recorded rather than silently corrected: Eshghi et al.'s Table S1 row #7 and swapped pair #23/#24 (datasets/odonata/NOTE_TO_AUTHORS.md) and PlanformDB experiment 434's control semantics (conflicting_control_semantics flag).

Extending the repository

A new reproduction is one script, one dataset folder, one audit. The 12 steps the loop tracks are the checklist; the first six are what you do, the last six are what MorphoEval does to it.

1. Scout and read the paper. Pick a published model of form, a formal database of forms, or a measurable claim. Decide which of the three kinds the script will be — reproduce the model from its equations, decode the authors' encoding, or test the claim — and say so in the docstring.
2. Vendor or pin the formal source. Create datasets/<name>/ with a README.md (source, licence, retrieval date, what was changed), paper_citations.bib, and either the files themselves (small, licence permitting) or their SHA-256 in a manifest with a --download path into a git-ignored .<name>_cache/ (add it to .gitignore). Record the hash of anything derived from the raw source (as datasets/conus/conus_textile_reference.json and datasets/planform/planform_bioelectric_series_v1.json do). Read the authors' code where it exists to settle what they meant; do not copy it.
3. Pin the rules. Turn the paper's prose into exact rules and verify them on every record before drawing anything (the Planform and Limbform decoders check their radius rule on all 1181 regions / 3146 joints at load time; the Raup script recovers W, D, T from its own mesh and refuses to draw if they differ).
4. Write <year>-<author>-<model>.py. Self-contained, run with python3, outputs (PNG/GIF/CSV) written to the working directory and git-ignored. Give it --self-test (deterministic checks, input hashes, fast), --gif PATH, a --no-show/offline path, and seeded RNGs. Put a real specimen or the authors' figure beside the output and measure the distance between them; distinct forms must come out distinct.
5. Make the media. Downsize the script's GIF into docs/media/ as described in docs/media/README.md and add a row there; re-run docs/media/make_montage.py and morphoeval/report/draw_pipeline.py --gif after adding the tile.
6. Document. Add the script to the index table and a section in this README (what it does, commands, "What you see", references), following the existing ones.
7. Audit. Copy the nearest morphoeval/audits/<date>-<name>.yaml, score the seven dimensions with line-pinned evidence at a recorded commit, and ideally have a second model from another company score it blind. python3 morphoeval/build_morphoeval_kg.py <audit> --check validates it; measure_outputs.py fingerprints and measures the outputs; build_morphoeval_kg.py --conform --query builds the nanopubs; sign_morphoeval.py signs (test registry first, then --publish prod); check_signed.mjs verifies independently. Commit morphoeval/kg/<audit>/ — it is the checkpoint. The full workflow, with the re-score and --supersede-from conventions, is in morphoeval/README.md.
8. State the mathematics. Add a section to morphoeval/lean/MathOfBiology.lean with a definition and at least one theorem per governing law (core Lean, no sorry; lean morphoeval/lean/MathOfBiology.lean must exit 0), and a matching entry in MATH_LAWS_REGISTRY in morphoeval/math_kg.py (formula, Lean declaration and theorem names, Lean and Python line loci, source equation). python3 morphoeval/math_kg.py --build then puts the law, its proof status and the audit's measurements into the graph; --sim <id> shows the result.
9. Track it (optional). morphoeval/track_loop.py init --run-id <id> --target <sim-id> then start/end or exec around each step; summary --md writes the per-step table (see morphoeval/runs/2026-10-18-runions-venation-loop.md for a complete worked sample run).

Re-scoring an existing script after a fix follows step 7 with a new audit file that names the one it supersedes; published nanopubs are never edited.

Analysis tools

Ca²⁺ Wave Vector Analysis

A complete pipeline for detecting and tracking Ca²⁺ signaling waves in time-lapse microscopy images of embryos. Processes multi-page TIFF images to detect bright spark events, track them across frames, segment embryos, and generate comprehensive analysis outputs. Includes visualization tools and supports 16-bit scientific imaging data.

See wave-vector-analysis/README.md for full documentation.

Spatial vector field showing wave propagation directions and speeds. This visualization complements standard analysis tools by providing spatial flow patterns not available in direction distribution plots.

Nanopublications

Nanopublication-related files including wave files (.trig format), hypothesis mappings, and scripts for processing and canonicalizing nanopublications. These tools enable structured representation and sharing of scientific findings in a machine-readable format. The MorphoEval nanopubs use their own signer and verifier (see morphoeval/README.md) because nanopub-py 2.1 does not work on Python 3.14.

See nanopubs/README.md for details.