{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:A3AXQSTJHEXHILDMB3ZRLOHGUA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9726409a9fad83c0210f3c4e419eced459d7d214215163e40467ef93125cd084","cross_cats_sorted":["hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-19T15:19:16Z","title_canon_sha256":"c427323c6a9cacca31ca1387b07ccd5451708eb45b503dd19a2e715c3d69966d"},"schema_version":"1.0","source":{"id":"2505.13236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13236","created_at":"2026-07-05T11:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13236v1","created_at":"2026-07-05T11:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13236","created_at":"2026-07-05T11:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"A3AXQSTJHEXH","created_at":"2026-07-05T11:05:27Z"},{"alias_kind":"pith_short_16","alias_value":"A3AXQSTJHEXHILDM","created_at":"2026-07-05T11:05:27Z"},{"alias_kind":"pith_short_8","alias_value":"A3AXQSTJ","created_at":"2026-07-05T11:05:27Z"}],"graph_snapshots":[{"event_id":"sha256:1d1e9aa9827876d0315c2fa912621ccaa6be12dfa5fd23348bd4d2359ed1b213","target":"graph","created_at":"2026-07-05T11:05:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.13236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order $d$. Here, we propose an extended theoretical framework for TFT that incorporates tensor fields of varying orders $d'$, satisfying $d' \\leq d$. We then establish a comprehensive group-theoretic formalism that enables the systematic enumeration of these complex TFT observables. This approach encompasses existing counting methods and therefore recovers known r","authors_text":"Arnauld Solente, Joseph Ben Geloun","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-19T15:19:16Z","title":"Multiple-Order Tensor Field Theory: Enumeration of unitary invariant observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13236","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:25751b04270790c6e229de31b8cf1cd1e79672b2b9578718e65c164ee8ef1849","target":"record","created_at":"2026-07-05T11:05:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9726409a9fad83c0210f3c4e419eced459d7d214215163e40467ef93125cd084","cross_cats_sorted":["hep-th","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-05-19T15:19:16Z","title_canon_sha256":"c427323c6a9cacca31ca1387b07ccd5451708eb45b503dd19a2e715c3d69966d"},"schema_version":"1.0","source":{"id":"2505.13236","kind":"arxiv","version":1}},"canonical_sha256":"06c1784a69392e742c6c0ef315b8e6a014f6e084fa844443159353833d740fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06c1784a69392e742c6c0ef315b8e6a014f6e084fa844443159353833d740fa6","first_computed_at":"2026-07-05T11:05:27.218155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:27.218155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WWfUWGQ6oietiyW+y2cWmMWMuLRTjGw3nx5wz+Jrg2ytpRAz2DorufwzzRgqVf+YGJtwSB+tn+oA5TPXR2CABg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:27.218659Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25751b04270790c6e229de31b8cf1cd1e79672b2b9578718e65c164ee8ef1849","sha256:1d1e9aa9827876d0315c2fa912621ccaa6be12dfa5fd23348bd4d2359ed1b213"],"state_sha256":"c8212baa828a6ae76c245c2a54fe2a3cf8a27545f167cec4c6e13b9a985ee494"}