feat(weave): construct and falsify native public/private polynomial candidate

[erinepshovel-code]

Construction and result

This replaces the off-target input-partition probe with an explicit mathematical candidate and working keygen, public-only sender, private inverse, and public recovery attack. The previous partition-only implementation and its controls are removed from the current tree.

A private source-bearing ByteOrigin and eight actual locked UCNS axes/complete states supply eight displacements. Whole-circle state 0 and occurrence-circle state 1 are published. Six hidden displacements define a cascade F_j(x) = (F_(j-1)(x) + a_(j+1))^2; its expanded degree-64 coefficients are the public evaluation law. The coefficient payload is fully disclosed and counted, not hidden behind the whole-plus-one label.

The sender runs the unchanged merged Weave cycle and evaluates the public polynomial on its exact length-bearing integer record. The recipient reconstructs private native states and reverses six exact square roots/subtractions before running the existing cycle inverse. No private argument, keygen call, callback or encoder trace enters the sender path.

Result: FALSIFIED for this candidate's private-state necessity. Exact coefficient decomposition recovers all six inverse displacements from the public key. A separate public-only process then recovers the original bytes without the private material. Public sending and private recovery both work; the required exclusivity fails. This is an actual candidate counterexample, not a verdict on intended Weave.

Boundaries

The binding is explicitly proposed Stack research over the completed cycle. It does not redefine UCNS geometry or assert completion of general higher-dimensional gonol construction. The private key-origin is separate from the cycle's retained message-origin. Sequence/occurrence construction, actual corpus bits, prime routes, all seven occurrence streams, native-source pins and existing cycle format are unchanged. No conventional cipher is substituted or security claimed. Effective hidden inverse space is at most 512^6; source-material size does not confer extra inverse entropy.

File plan

Files	Change	Purpose / risk	Verification
research/weave/private_public.py	Replace prior probe	Native candidate keygen, public polynomial, private roots, algebraic attack; research only	20 candidate regressions
research/weave/tests/test_private_public.py	Replace prior tests	Native dependence, exact recovery, public decomposition, separate processes, malformed inputs and failure gate	Full Weave suite
research/weave/PRIVATE_PUBLIC.md, README.md, QUESTIONS.md	Update	Defined law, frozen falsifier, source boundaries, usage and rollback	Source review
research/weave/evidence/private-public-v1.json	Regenerate	Current candidate receipt and complete size accounting	Actual CLI execution
research/weave/test.py, .github/workflows/weave.yml	Update	Suite coverage and reproduction of the expected failing distinction gate	Local suite / hosted CI

Verification

• 196 tests passed, zero failures/errors/skips, unchanged tested source; includes 20 actual candidate tests and three-process execution with fresh system-random private material.
• Suite source SHA-256: b43b7329099175e54d0ac2eb7a6850bbe870e7ddd898027243fb6e6fa609a0f3.
• Public/private polynomial equality, exact inverse, and public decomposition checked for 32 deterministic displacement tuples; all eight native states tested for actual effect on binding.
• Six source obligations / twenty witnesses; ratio seals and Stack consistency passed.
• --require-distinction exits 1 because public recovery succeeds; malformed inputs or infrastructure failure exit 2.
• Published tree e47c61afd257a28c238e2fddfbf3fe8dcb342564 matches tested local bytes exactly.
• Demo: 14 message bytes → 5,904 inner-cycle bytes → 377,885 packet bytes; public artifact 8,091 bytes, private artifact 572 bytes. No fixed expansion or compression claim.

Usage

cd research/weave
python private_public.py --sources /checkouts
python private_public.py --sources /checkouts --require-distinction
WEAVE_SOURCES=/checkouts python test.py --receipt /tmp/weave-check.json

Python standard library and the existing locked UCNS source only. Remove the candidate and links to roll back; the merged cycle remains intact. A green regression run reproduces the candidate's negative scientific result.

hmmm

A surviving native asymmetric relation remains unestablished. This candidate exposes an equivalent inverse through its public coefficients. Confidentiality, authentication, replay and broader private-corpus binding are not supplied.