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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

Same final Pin geometry retains history with an unchanged index factor

In the question: Common clock sectors, quartic geometry and operational reconstruction

Exact transported pair identity on the full given source;pulse values from a finite129-mode run with chosen duration/amplitude. No cyclic cutoff shift as an index proof. Full P1 measure/reference Ward identification remains open;the relative CAR response is not substituted into delta logR without proof.

Read the exact result, assumptions and evidence

Result

For the two actual commonly evolved states P_t=U C0 U*,Q_t=P_t+Pi_t and exactly(I-zQ_t)(I-zP_t)^-1=I-zPi_t,determinant1-z,without requiringC_t-C0 inL1. After50 pulse steps and50 steps with exactly restored D0,the t1 relative readouts differ:no pulse-.4739486483,positive+.01-.4701253569,negative-.01-.4780397086. Recursion matches direct evolution to4.8e-14. Causal kernel predicts pulse derivative.3956885828,finite symmetric difference.3957175880. Complete historical sector weight remainsQ_full=e^-2alpha R(g,alpha);its geometry response at fixed alpha comes fromR and is not calculated by the index.

Required assumptions

  • Retained zero-branch defect on a common Pin geometry history

    The original normal-zero branch k=pi/2,b1,c+i carries the retained positive quarter defect Pi. Compare the given pure D0 sea C0 and C0+Pi,both evolved by the same D_s=exp(-s h/2)D0 exp(-s h/2). The profile and tested step/pulse histories are named diagnostic inputs. Relative geometry response is Tr(U Pi U* partial_sD_s). It is not defined into the primitive P1 action response or a thin local seam map.

  • Given flat Moebius Dirac boundary family and its full sea

    The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.

  • Controlled conformal normal geometry of the given Pin Dirac source

    For the authorized source study,the same given Dirac comparison D0 on its fixed(c,b)Pin/boundary domain is varied by smooth real even profiles h:g_e=exp(2e h)g0,D_e=exp(-e h/2)D0 exp(-e h/2)after unitary density transport. Profiles/amplitude are explicitly chosen diagnostic interventions,not a P1-selected history. Original pure D0 sea remains initial state;thermal Green quantization stays separate.

  • Do not identify source types

    Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

  • Historical SF sector action and explicit relative normalization

    fullv27/v28 set J1=SF,J=d SF,d2,SF1 in S_def(alpha)=S_def0+alpha J. Review concerns the intended defect-only relative reweighting and its extension to complete measure-compatible sectors Z_s=e^(-alpha d s)Z_s^0(alpha),Z0=Z0^0(alpha). Constancy of R=Z_s^0/Z0^0 is an explicit condition, not assumed from SF.

Original evidence

  • GEOMETRIC-SECTOR-RESPONSE.txt lines 1–194

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/GEOMETRIC-SECTOR-RESPONSE.txt

    8ba1f1e255a40b90888e47b95b1ec555ff5af051b49fd70b4d8336cd497a8197

  • check_geometric_sector_response.py lines 1–167

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/geometric_sector_response/check_geometric_sector_response.py

    a0a151e05bff917c1ea2c971e24d2b6f00b304e5b43502267200833ca3bc49f8

  • geometric_sector_response.json lines 1–145

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/geometric_sector_response/geometric_sector_response.json

    fe35987cd8349b7e9772264da859e05a3582ae4a2acab7320e49464328a3dedf

  • DIRECT-DEFECT-CLOSURE.txt lines 22–132

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/DIRECT-DEFECT-CLOSURE.txt

    84a79c74da8b18387a3d2d8a9928e4a437a608120b52a46c7ede6392cf1128ff

  • PAIR-INDEX-DETERMINANT.txt lines 26–78

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/PAIR-INDEX-DETERMINANT.txt

    7c7dc9d48a96a140afeb72ddb2d0e6ae2f37e73e6260426544b9a94d7abac04d

  • REWEIGHTING-REVIEW.txt lines 43–149

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/REWEIGHTING-REVIEW.txt

    aa7479fc2d4bb9eb11fd071e81550906bd4105e43a19af759da7054efbc3d49a

finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed