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Non-perturbative spectral gravity measure in the Hilbert-Schmidt Gaussian completion: pro-torsor structure and the obstruction to canonical expectations

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Issuer
did:web:openxiv.net
Verification method
did:web:openxiv.net#atproto
Generated
5/22/2026, 9:59:23 PM
Evidence digest
sha256-1miz0Tedf3MZvw8jxtRsiDe4B0v6diKWhBQroJL25cw
Signature
DxVZ1LZywG2TOHkdIyxND1XaTL_pHFONsr4T6O-ReDdZYzbGV4JiFzLlbMkXQ9KtXszclyeiV0Ksb87YYtsu-A
Transparency openxiv-transparency-v1.0 Partial
Evidence summary OpenXiv checks 4 verified 1 need attention

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  • Structured AI-use disclosure Verified Author submitted the formal AI-use questionnaire. Action: Submit the structured AI-use disclosure.
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Identity openxiv-identity-v1.0 Strong
Evidence summary OpenXiv checks 4 verified
  • Submitter DID parses as resolvable Verified Submitter signs with a did:plc or did:web identity. Action: Publish under a valid did:plc or did:web identity.
  • At least one ORCID-identified author Verified One or more authors have an ORCID iD attached. Action: Attach ORCID iDs for at least one author, ideally all authors.
  • Author identity coverage Verified 2/2 authors have ORCID or DID evidence. Action: Attach ORCID or DID evidence to every author row.
  • Author list present Verified 2 author rows recorded. Action: Record the author list before publication.
Provenance openxiv-provenance-v1.0 Strong
Evidence summary OpenXiv checks 4 verified 1 pending

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  • Lifecycle provenance completion Pending Lifecycle timeline has not been computed yet. Action: Recompute the provenance timeline.
Citations openxiv-citations-v1.0 Strong
Evidence summary OpenXiv checks 27 verified 4 need attention

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  • Citation {CC:1996} Verified Resolved {CC:1996} via DOI. {CC:1996} 10.1103/PhysRevLett.77.4868 doi high confidence
  • Citation {CC:1997} Verified Resolved {CC:1997} via DOI. {CC:1997} 10.1007/s002200050126 doi high confidence
  • Citation {CCM:2007} Verified Resolved {CCM:2007} via DOI. {CCM:2007} 10.4310/ATMP.2007.v11.n6.a3 doi high confidence
  • Citation {vS:2015} Verified Resolved {vS:2015} via DOI. {vS:2015} 10.1007/978-94-017-9162-5 doi high confidence
  • Citation {BarrettGlaser:2016} Verified Resolved {BarrettGlaser:2016} via DOI. {BarrettGlaser:2016} 10.1088/1751-8113/49/24/245001 doi high confidence
  • Citation {AzarfarKhalkhali:2024} Verified Resolved {AzarfarKhalkhali:2024} via DOI. {AzarfarKhalkhali:2024} 10.4171/AIHPD/188 doi high confidence
  • Citation {PerezSanchez:2021} Verified Resolved {PerezSanchez:2021} via DOI. {PerezSanchez:2021} 10.1007/s00023-021-01025-4 doi high confidence
  • Citation {vNvS:2022} Verified Resolved {vNvS:2022} via DOI. {vNvS:2022} 10.1007/JHEP05(2022)078 doi high confidence
  • Citation {Surya:2019} Verified Resolved {Surya:2019} via DOI. {Surya:2019} 10.1007/s41114-019-0023-1 doi high confidence
  • Citation {AJL:2012} Verified Resolved {AJL:2012} via DOI. {AJL:2012} 10.1016/j.physrep.2012.03.007 doi high confidence
  • Citation {Anselmi:2018} Verified Resolved {Anselmi:2018} via DOI. {Anselmi:2018} 10.1007/JHEP02(2018)141 doi high confidence
  • Citation {Bogachev:1998} Verified Resolved {Bogachev:1998} via DOI. {Bogachev:1998} 10.1090/surv/062 doi high confidence
  • Citation {Kuo:1975} Verified Resolved {Kuo:1975} via DOI. {Kuo:1975} 10.1007/BFb0082007 doi high confidence
  • Citation {Alfyorov:2026ff} Verified Resolved {Alfyorov:2026ff} via DOI. {Alfyorov:2026ff} 10.22541/au.177507193.33027854/v1 doi high confidence
  • Citation {Donoghue:1994} Verified Resolved {Donoghue:1994} via DOI. {Donoghue:1994} 10.1103/PhysRevD.50.3874 doi high confidence
  • Citation {Alfyorov:2026ss} Verified Resolved {Alfyorov:2026ss} via DOI. {Alfyorov:2026ss} 10.22541/au.177524450.03515205/v1 doi high confidence
  • Citation {Alfyorov:2026ct} Verified Resolved {Alfyorov:2026ct} via DOI. {Alfyorov:2026ct} 10.22541/au.177516440.00576784/v1 doi high confidence
  • Citation {AlfyorovShnyukov:2026ns} Verified Resolved {AlfyorovShnyukov:2026ns} via DOI. {AlfyorovShnyukov:2026ns} 10.13140/RG.2.2.13540.74886 doi high confidence
  • Citation {% AlfyorovShnyukov:2026ns} Needs attention Reference entry not found in extracted bibliography. {% AlfyorovShnyukov:2026ns} unresolved unresolved low confidence Reference entry not found in extracted bibliography. Action: Add a DOI, arXiv id, or stable URL to this reference.
  • Citation {Feldman:1958} Verified Resolved {Feldman:1958} via DOI. {Feldman:1958} 10.2140/pjm.1958.8.699 doi high confidence
  • Citation {Hajek:1958} Needs attention No DOI, arXiv, or stable URL found in reference entry. {Hajek:1958} unresolved unresolved low confidence No DOI, arXiv, or stable URL found in reference entry. Action: Add a DOI, arXiv id, or stable URL to this reference.
  • Citation {Parthasarathy:1967} Verified Resolved {Parthasarathy:1967} via DOI. {Parthasarathy:1967} 10.1016/C2013-0-08107-8 doi high confidence
  • Citation {Vassilevich:2003} Verified Resolved {Vassilevich:2003} via DOI. {Vassilevich:2003} 10.1016/j.physrep.2003.09.002 doi high confidence
  • Citation {CPR:2009} Verified Resolved {CPR:2009} via DOI. {CPR:2009} 10.1016/j.aop.2008.08.008 doi high confidence
  • Citation {CZ:2013} Verified Resolved {CZ:2013} via DOI. {CZ:2013} 10.1063/1.4776234 doi high confidence
  • Citation {AJL:2005} Verified Resolved {AJL:2005} via DOI. {AJL:2005} 10.1103/PhysRevLett.95.171301 doi high confidence
  • Citation {Anselmi:2020} Verified Resolved {Anselmi:2020} via DOI. {Anselmi:2020} 10.1088/1361-6382/ab04c8 doi high confidence
  • Citation {% Alfyorov:2026fe} Needs attention Reference entry not found in extracted bibliography. {% Alfyorov:2026fe} unresolved unresolved low confidence Reference entry not found in extracted bibliography. Action: Add a DOI, arXiv id, or stable URL to this reference.
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  • Citation {AAS:2012} Verified Resolved {AAS:2012} via DOI. {AAS:2012} 10.1007/JHEP08(2012)137 doi high confidence
  • Citation {ParkerToms:2009} Verified Resolved {ParkerToms:2009} via DOI. {ParkerToms:2009} 10.1017/CBO9780511813924 doi high confidence
Math openxiv-math-v1.0 Partial
Evidence summary OpenXiv checks 7 verified 1 need attention

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  • Formula evidence 1 Verified Formula-like expression found in Untitled section. formula Untitled section medium confidence \(\Phi\)
  • Formal structure 1 Verified Formal statement/proof cue found in Untitled section. formal statement Untitled section medium confidence We prove a principal no-section theorem: relative to any choice of reference weight \(\Phi\), the bounded density gauge group acts freely on normalized projective representatives, precluding further canonical reduction...
  • Formal structure 2 Verified Formal statement/proof cue found in Untitled section. formal statement Untitled section medium confidence The authors prove a “no‑section theorem,” showing that no single choice of reference can produce a unique, background‑independent probability measure without adding extra mathematical structure.
  • Formal structure 3 Verified Formal statement/proof cue found in Untitled section. formal statement Untitled section medium confidence The authors prove a no-go theorem: without adding extra structure, there is no way to pick a distinguished, scalar probability measure from this collection—any attempt either reduces to a tautology or fails.
  • Formal structure 4 Verified Formal statement/proof cue found in Untitled section. formal statement Untitled section medium confidence A no-section theorem shows that the bounded density gauge group acts freely on normalized projective representatives, precluding canonical reduction to a scalar probability without extra structure.
  • Formal structure 5 Verified Formal statement/proof cue found in Untitled section. formal statement Untitled section medium confidence The results are confined to Dirac operators with compact resolvent, and the finite-rank no-go theorem shows that trivial scalar reduction is inherently tautological within this framework. spectral theorem not measure ga...
  • Source archive for math audit Verified Source archive is retained for independent formula and derivation checks. source archive high confidence
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Integrity openxiv-integrity-v1.0 Partial
Evidence summary OpenXiv checks 2 verified 1 need attention 1 not applicable

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  • Undisclosed-AI detector Not applicable Detector is not used as a penalty because the author disclosed AI use.
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Social Review openxiv-social-review-v1.0 Pending
Evidence summary OpenXiv checks 0 verified 2 need attention 1 not applicable

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