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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

Actual Fuchs halfpath has a canonical G-metric C6 kernel map

In the question: Automated construction of operator maps and sources

Positive finite ORIGINALpath with transported endpoints and every already givenPstr. No fitted/free metric or rawEuclideanadjoint identification. Read preliminarytype review with positiveGmetric addendum. Transportfiber pair need not equalF5faces; sheetparity is not automaticallyCalderonpolarization. No equality of geometricR/nativeclock/U6 by order. Wordtraces concern only certifiedcontribution. ActualZadm/blockedT insertion,entireD4spine and originalendpoints/compression remain at their originalconsumer. K is coupling,not a universalCARmap. GivenwholeG/W state/reflection/time remain; fullphysicalorigin/time derivation is not proved. StrongerBstar also retains originalquartermark; a single-M eigenbasis match alone would not. Common scalarphase cancels in endomorphisms. Transport full96J_F/Clifford/marks with the complex basis. κP0 is not identified with entirepositiveKstr, and actual originalsource insertion remains to execute. diag(kappaM0P0,0) is explicitly a comparisonembedding, not a derivedwhole6Hardysource or physicalzero for otherbranches. Any already givenwhole6operator andcross/adjointlegs share the sameEfold. Do not reopen nine free addresses or a new Hitchin PDE. Retain conditional margin provenance, distinguish native1/2 from later delta_ph, and do not turn scalar readout into whole-Yukawa or insertion provenance.

Read the exact result, assumptions and evidence

Result

Actual originalv117 P/Q integration and separately exact unitarykernel now share a closed frame map using already proved algebraicG. Fixed H=G^-dagG^-1 source metric and actualsigned cycleCs give Cpair^-1TrawCpair=[[0,Cs],[I,0]] with Cpair=diag(Gx,PGx) an isometry. Sourceadjoint equalsinverse. ExplicitB and existingJ connect to originalM/U6. Actualpath,D,metricGram,Green and inverse square root share one isometricfinite map, independently replayed with realP/Q residuals<1.3e−12. EvenwordCs² reads certifiedκE02 contribution; barepositiveK branch weights give v±κ. These are evaluated contributions, not an assertion that the complete originalsource inserted them. Stronger common marked closure: originalGbase/H0 gives H0^1/2Gbase=e^(7pi i/12)Bstar with explicitly fixed unitaryBstar. The sameBstar intertwines both actualCs to originalM0 and inverseKQ to originalU, hence all four markedmeridians. Exactly BstarE02Bstar†=M0P0 and BstarE22Bstar†=P0. CertifiedHardy contribution is thusκM0P0 in the common originalmarked frame with the existing quarter-fixede0 input. Six exact rootidentities and literalGbase normalization replay confirm it. The fixed markedendpoint is explicitly P0=(I+U²)/2; separately reviewed findings continue this same channel through the actualreal delta jet and allfour originalopenpaths. Positive actualspine consumer: originalP/Q fold is realized by P=T3,Q=T0^-1 and fixedC, with sameJ carrying inversefold to originalU6. OriginalD_y/fullGram/positivefunctionalcalculus and every already givenPstr transport isometrically; eight independent rootsymbolic checks pass. Recovered original v118 consumer reads det(I-tM0)=1-t³; native t=1/2 gives16/7,4/3,7/6. Later v121/FLAV.H2.04 uniquely pins recorded R under declared margins anddet8 among17 candidates, independently re-enumerated.

Required assumptions

  • 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.

  • Unchanged A0* Fuchsian equation and actual C4 clock

    Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.

  • Recovered genus2 cover with retained coefficients

    Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.

  • Supplied split carrier with actual q sign lines on genus-two cover

    Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.

  • Relative spin and reference Hardy cable on original three-cover

    Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.

  • Original hard-holonomy contract with pure closed-triangle trace

    Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.

Original evidence

  • ACTUAL-FUCHS-PATH-C6-HARDY-CONSUMER.txt lines 1–190

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ACTUAL-FUCHS-PATH-C6-HARDY-CONSUMER.txt

    99d7aafa1e204f344f00b6d1fc6344ed7895295b01f847674422a97784735ed8

  • FLAVOR-PATH-TRANSPORT-SOURCE-TYPE-REVIEW.txt lines 1–120

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FLAVOR-PATH-TRANSPORT-SOURCE-TYPE-REVIEW.txt

    23e11fb0309b5260c8cf9049b438a567724ab8342e77d18940289f5017257067

  • FLAVOR-PATH-TRANSPORT-G-METRIC-ADDENDUM.txt lines 1–118

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FLAVOR-PATH-TRANSPORT-G-METRIC-ADDENDUM.txt

    2630f1de582645bef554537c6c16aa8004dfeff83631097a4850aa502c85c443

  • ROOT-ACTUAL-PATH-G-METRIC-REVIEW.txt lines 1–78

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ACTUAL-PATH-G-METRIC-REVIEW.txt

    bd84febd1cd122b5145bb918553f6d9cdab5c4e89fb6601c1f3da11b51b184f0

  • ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt lines 1–174

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt

    3a57907902631b58e0abee61e9a424c3ac03ff7a8fa074cc4d27e3379b406cf3

  • flavor_path_transport.py lines 70–199

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    Original location and fingerprint

    tfpt_explorer/flavor_path_transport.py

    82b4fab94138ab3f5122cf40d507e7a4b7c8a5da25393d4f42dcd35259a9de92

  • ROOT-COMMON-MARKED-FUCHS-HARDY-REVIEW.txt lines 1–50

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-COMMON-MARKED-FUCHS-HARDY-REVIEW.txt

    a085f6735da10cafa35e31d9548323d83de628c6ae304cc5ae1c78056fc57bb9

  • FULL-MARKED-G-FRAME-AND-ORIGINAL-OPEN-WORD.txt lines 1–160

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FULL-MARKED-G-FRAME-AND-ORIGINAL-OPEN-WORD.txt

    1090dbaa4bb2ab7bf3ed1f6cebbe4498bf794cd51e6e103502948c9f614e914e

  • SPINE-ORIGINAL-PQ-FOLD-KERNEL-ADDENDUM.txt lines 1–143

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPINE-ORIGINAL-PQ-FOLD-KERNEL-ADDENDUM.txt

    d98da73f0023e1de696a31874d73b1df547564cec70205c07e5a54f3e0dc0fc5

  • ROOT-SPINE-FOLD-C6-CONSUMER-REVIEW.txt lines 1–45

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-REVIEW.txt

    fb1d8858d1e90ac5cad5b80777b620162bfb8c14b0ebffbe6112e7bf661fef14

  • ROOT-SPINE-FOLD-C6-CONSUMER-CHECK.json lines 1–11

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-CHECK.json

    c18e4e48e8d4bba9bab3a0aef23a4078774ef8ceaae5b4b9e42962a086f99a43

  • RECOVERED-ORIGINAL-RESOLVENT-AND-WORD-READOUT.txt lines 1–51

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/RECOVERED-ORIGINAL-RESOLVENT-AND-WORD-READOUT.txt

    d44c6f0172c5030a7b84056849a61d74d70346fed35b933a5f2bd919763d9d26

  • ROOT-RECOVERED-V118-V121-READOUT-CHECK.json lines 1–64

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    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-RECOVERED-V118-V121-READOUT-CHECK.json

    9eb5a7f60c898f99bbc6a09321c8c68bdee83b023c180531d3def2ecff19d06b

  • 006-source.tex lines 236–258

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    Original location and fingerprint

    documents/tfpt_research_contracts/sections/006-source.tex

    a93b3c1fd9be52521a3eea6ca82b6bddd16e15c2447382f274d3542a36a0382b

  • v118_hexagon_family_dictionary.py lines 54–138

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    Original location and fingerprint

    verification/v118_hexagon_family_dictionary.py

    48b7a05bcd877afe13f0a92cce4087e86c23172823e605cda21c6a8ceafa6e37

  • status_ledger.csv lines 205–205

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    Original location and fingerprint

    verification/status_ledger.csv

    8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4

finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map