{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OJVOOGZ3NU5YP3UWSMJE73G2K5","short_pith_number":"pith:OJVOOGZ3","canonical_record":{"source":{"id":"2108.10979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-24T22:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"4879682dfb5cb64cc415d842588977cd02ec49893728d5eb5deb3730f8de9484","abstract_canon_sha256":"4f1916293d45655205ac4c2be656719709716aa4fcc53c2496e2b323d7ee5add"},"schema_version":"1.0"},"canonical_sha256":"726ae71b3b6d3b87ee9693124fecda577389bcec9518c487fd6b751d9b71421e","source":{"kind":"arxiv","id":"2108.10979","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.10979","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"arxiv_version","alias_value":"2108.10979v2","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.10979","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"pith_short_12","alias_value":"OJVOOGZ3NU5Y","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"pith_short_16","alias_value":"OJVOOGZ3NU5YP3UW","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"pith_short_8","alias_value":"OJVOOGZ3","created_at":"2026-07-05T03:58:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OJVOOGZ3NU5YP3UWSMJE73G2K5","target":"record","payload":{"canonical_record":{"source":{"id":"2108.10979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-24T22:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"4879682dfb5cb64cc415d842588977cd02ec49893728d5eb5deb3730f8de9484","abstract_canon_sha256":"4f1916293d45655205ac4c2be656719709716aa4fcc53c2496e2b323d7ee5add"},"schema_version":"1.0"},"canonical_sha256":"726ae71b3b6d3b87ee9693124fecda577389bcec9518c487fd6b751d9b71421e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:58:17.113794Z","signature_b64":"m/exHYqtMj5hAFT0Yyk1cYKzKr5DcvYNTAZvq154E4ne40v2yaR4xDrB01STEYPSxP3c2/Zu+nqz+3loHyvBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"726ae71b3b6d3b87ee9693124fecda577389bcec9518c487fd6b751d9b71421e","last_reissued_at":"2026-07-05T03:58:17.113285Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:58:17.113285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.10979","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:58:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2BzkXMLhKHK0112u7y8g0PWzEWIBW98/yRkVtI0MGncWEcGtONqxJw668k9HBeIJ0R4N+kHlYZMpkc1ygrFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:35:07.655886Z"},"content_sha256":"a6bcc8acb013acf6ff059cd9edb98f483816aee6f4c9cd8f6f859b97b3aa13e3","schema_version":"1.0","event_id":"sha256:a6bcc8acb013acf6ff059cd9edb98f483816aee6f4c9cd8f6f859b97b3aa13e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OJVOOGZ3NU5YP3UWSMJE73G2K5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"B\\^em-Bi\\'eri Barth\\'el\\'emy Natta, Dine Ousmane Samary, Vincent Lahoche","submitted_at":"2021-08-24T22:34:05Z","abstract_excerpt":"This paper aims at investigating the nonperturbative functional renormalization group for tensorial group field theories with nontrivial kinetic action and closure constraint. We consider the quartic melonic just-renormalizable $[U(1)]^6$ model and show that due to this closure constraint the first order Ward-Takahashi identity takes the trivial form as for the models with propagators proportional to identity. We then construct the new version of the effective vertex expansion applicable to this class of models, which in particular allows to close the hierarchical structure of the flow equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.10979","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.10979/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:58:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKQJwzwXWcRx1YKDnI/bcI9EYigsMJi688XCU8jDLIg5Y0E6ySgsrwWKXvBb3Zk1jYFpC1Ubcnx54K5DeasaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:35:07.656509Z"},"content_sha256":"88cbb0fa0908e082d24dcb17155310384c2f4bc7726a6d7f37889c8bd5dd45a8","schema_version":"1.0","event_id":"sha256:88cbb0fa0908e082d24dcb17155310384c2f4bc7726a6d7f37889c8bd5dd45a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5/bundle.json","state_url":"https://pith.science/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T02:35:07Z","links":{"resolver":"https://pith.science/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5","bundle":"https://pith.science/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5/bundle.json","state":"https://pith.science/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJVOOGZ3NU5YP3UWSMJE73G2K5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OJVOOGZ3NU5YP3UWSMJE73G2K5","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":"4f1916293d45655205ac4c2be656719709716aa4fcc53c2496e2b323d7ee5add","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-24T22:34:05Z","title_canon_sha256":"4879682dfb5cb64cc415d842588977cd02ec49893728d5eb5deb3730f8de9484"},"schema_version":"1.0","source":{"id":"2108.10979","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.10979","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"arxiv_version","alias_value":"2108.10979v2","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.10979","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"pith_short_12","alias_value":"OJVOOGZ3NU5Y","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"pith_short_16","alias_value":"OJVOOGZ3NU5YP3UW","created_at":"2026-07-05T03:58:17Z"},{"alias_kind":"pith_short_8","alias_value":"OJVOOGZ3","created_at":"2026-07-05T03:58:17Z"}],"graph_snapshots":[{"event_id":"sha256:88cbb0fa0908e082d24dcb17155310384c2f4bc7726a6d7f37889c8bd5dd45a8","target":"graph","created_at":"2026-07-05T03:58:17Z","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/2108.10979/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper aims at investigating the nonperturbative functional renormalization group for tensorial group field theories with nontrivial kinetic action and closure constraint. We consider the quartic melonic just-renormalizable $[U(1)]^6$ model and show that due to this closure constraint the first order Ward-Takahashi identity takes the trivial form as for the models with propagators proportional to identity. We then construct the new version of the effective vertex expansion applicable to this class of models, which in particular allows to close the hierarchical structure of the flow equatio","authors_text":"B\\^em-Bi\\'eri Barth\\'el\\'emy Natta, Dine Ousmane Samary, Vincent Lahoche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-24T22:34:05Z","title":"No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.10979","kind":"arxiv","version":2},"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:a6bcc8acb013acf6ff059cd9edb98f483816aee6f4c9cd8f6f859b97b3aa13e3","target":"record","created_at":"2026-07-05T03:58:17Z","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":"4f1916293d45655205ac4c2be656719709716aa4fcc53c2496e2b323d7ee5add","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-08-24T22:34:05Z","title_canon_sha256":"4879682dfb5cb64cc415d842588977cd02ec49893728d5eb5deb3730f8de9484"},"schema_version":"1.0","source":{"id":"2108.10979","kind":"arxiv","version":2}},"canonical_sha256":"726ae71b3b6d3b87ee9693124fecda577389bcec9518c487fd6b751d9b71421e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"726ae71b3b6d3b87ee9693124fecda577389bcec9518c487fd6b751d9b71421e","first_computed_at":"2026-07-05T03:58:17.113285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:58:17.113285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m/exHYqtMj5hAFT0Yyk1cYKzKr5DcvYNTAZvq154E4ne40v2yaR4xDrB01STEYPSxP3c2/Zu+nqz+3loHyvBDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:58:17.113794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.10979","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6bcc8acb013acf6ff059cd9edb98f483816aee6f4c9cd8f6f859b97b3aa13e3","sha256:88cbb0fa0908e082d24dcb17155310384c2f4bc7726a6d7f37889c8bd5dd45a8"],"state_sha256":"66d81d5b9b870306e8ce6b6ad929a4962e377c0c3678dfc060643bd5a94e05bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E8TDngsmXBUs6mr1K3ROW2dfYr1v9IGcXrhHUQVBOYW/71Mr6uWQT/muaCXPIsVh2ShArg+uK0VL9BPRgF5lAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T02:35:07.660880Z","bundle_sha256":"8e665ebd02fb1688abeccd428fe06fb04e3452e400475e0cf65531fb3ee4ecdd"}}