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Which seam action distinguishes native opposite charges?

Can existing native charge fields produce the quarter-twist time response of the seam?

What was learnedReviewed results and their assumptions What was triedApproaches and recorded conclusions What remainsTasks and explicit dependencies

What has been learned

Scoped exclusion

Fixed hopping phases do not produce the required asymmetry

In the question: Which seam action distinguishes native opposite charges?

Fixed phases and corresponding invariant starts; real time retains conjugation/time reversal. No assertion about all P1/P2 sources.

Read the exact result, assumptions and evidence

Result

C and K may separately break; A=CK preserves H for all fixed link phases and T_p→T_−p. Invariant starts retain equal Euclidean opposite-charge returns, including quarter phases/flux.

Required assumptions

Full original charge-field source
Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed.
Fixed link phases and A-invariant start
Arbitrary fixed unitary link phases in the same hopping, real original Hdiag/cocycle and initial density invariant under A=C times complex conjugation. Positive Euclidean T return responses are considered; no general real-time equality is assumed.
Fixed nonzero chiral quarter twist
The comparison target is the stipulated Kδ Fock space with original nonzero quarter twist, normalized ±Bp primary states, fixed charge marking and the same positive time. Equality of all these responses is required.

Original evidence

ADDENDUM.md lines 1–149
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-charged-conjugation-20261015/ADDENDUM.md
9c29c633efacdd7e7a043f1121076d14cb0f2bf8706d8250f9a734c9d409ad2b

finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator

Established in scope

C0 does not hide charged intermediate sectors

In the question: Which seam action distinguishes native opposite charges?

Balanced W remain within the sector; T insertion/removal responses require Cp. No derived physical measuring instrument.

Read the exact result, assumptions and evidence

Result

η·Qtot is zero on C0. T_p enters Cp; full propagation yields ratio exp(−2tη·p). For v=Bp, conditionally η=Bᵀδ. Only the odd factor is matched.

Required assumptions

Full original charge-field source
Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed.
Chemical comparison with charged intermediate sectors
Additionally supplied Hη=H+η·Qtot, C-invariant initial density in C0 and full propagation after onsite T moves C0 into Cp. η is comparison input, not a derived seam parameter.

Original evidence

PROOF.md lines 1–178
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-charged-conjugation-20261015/PROOF.md
db1da5ce443535c1972bb93314f4478a1e0627b0a0524501d4166f41feb56024

finding:native-chemical-mark-visible-in-charged-corners

Established in scope

Native fields exist; opposite-charge responses agree

In the question: Which seam action distinguishes native opposite charges?

Unchanged finite source and specified invariant start; different states or operator dictionaries are not excluded.

Read the exact result, assumptions and evidence

Result

Original C T_p C=T_−p, T_p*=(-1)^e(p)T_−p and C H C=H. At an invariant start all C-conjugate bounded words agree.

Required assumptions

Full original charge-field source
Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed.
Charge-conjugation-invariant start
The initial density is invariant under linear C:n→−n, including full and C0 Gibbs starts of unchanged H. Compare actual adjoint-paired, opposite marked T responses at the same time.

Original evidence

PROOF.md lines 1–178
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-charged-conjugation-20261015/PROOF.md
db1da5ce443535c1972bb93314f4478a1e0627b0a0524501d4166f41feb56024

finding:native-opposite-charge-response-symmetry

Scoped exclusion

Unchanged native source is not the fixed chiral response

In the question: Which seam action distinguishes native opposite charges?

Only the fixed marked response identification at these starts and the same time.

Read the exact result, assumptions and evidence

Result

The native ratio is one; the fixed quarter twist gives exp(−2tδ·Bp), which differs from one on at least one original basis direction.

Required assumptions

Full original charge-field source
Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed.
Charge-conjugation-invariant start
The initial density is invariant under linear C:n→−n, including full and C0 Gibbs starts of unchanged H. Compare actual adjoint-paired, opposite marked T responses at the same time.
Fixed nonzero chiral quarter twist
The comparison target is the stipulated Kδ Fock space with original nonzero quarter twist, normalized ±Bp primary states, fixed charge marking and the same positive time. Equality of all these responses is required.

Original evidence

PROOF.md lines 1–178
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-charged-conjugation-20261015/PROOF.md
db1da5ce443535c1972bb93314f4478a1e0627b0a0524501d4166f41feb56024

finding:native-invariant-response-not-fixed-chiral-twist

Approaches and conclusions

The reviewed decision record says which approach can be reused, which failed in its scope and what a new attempt would have to change.

Scoped exclusion

Read unchanged native response as a single twist

Equal plus/minus ratio contradicts the nonzero fixed twist.

Consequence: Justify an actual change of state, source operator or marked field map.

Supporting result

Scoped exclusion

Add a quarter phase only to hopping

A=CK survives; the discriminating Euclidean response remains symmetric.

Consequence: A seam-derived A-breaking operator or initial state changes the premise.

Supporting result

Reusable result

Reuse native charged-corner ratio

The exact ratio formula is available; C0 must include the charged corners for this purpose.

Consequence: A different charge action or nonuniform marking requires a new calculation.

Supporting result

What is resolved, and what remains

Resolved in scope

Check native fields and response discriminator

Explicitly retain T, actual adjoints and both propagation sectors.

Read the resolving result

Open task

Derive actual marked seam/state action

The same original source supplies the marked field/state/time dictionary and its odd charged response.

Next investigation: Test at the actual seam operator or selected state how the established symmetry is avoided; prescribing η is insufficient.

Builds on: Check native fields and response discriminator

Connections to other questions

constrains under

Which responses distinguish charged time action?

Charged Fock discriminator tested on original native T fields.

constrains under

Historical: common source, state and event selection

The common seam/state map must account for this response symmetry.

Original historical attempts linked to this question

These are original research records. Their reported verdicts are distinct from the reviewed results above.