{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BGK2566POZFUL7U6H776PZXYPN","short_pith_number":"pith:BGK2566P","canonical_record":{"source":{"id":"1411.3180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T14:10:22Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"b0a7caf5fed72bb68a3e85280a2ae1ad417d263e46fde7ddf842ed42cc8cbbf9","abstract_canon_sha256":"e38a7d065fa3d68f348951fa410e8c25684ce6c469608711034c880035e74e1f"},"schema_version":"1.0"},"canonical_sha256":"0995aefbcf764b45fe9e3fffe7e6f87b7f710502afc32f4287e323610a4bfc65","source":{"kind":"arxiv","id":"1411.3180","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3180","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3180v2","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3180","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"BGK2566POZFU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BGK2566POZFUL7U6","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BGK2566P","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BGK2566POZFUL7U6H776PZXYPN","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T14:10:22Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"b0a7caf5fed72bb68a3e85280a2ae1ad417d263e46fde7ddf842ed42cc8cbbf9","abstract_canon_sha256":"e38a7d065fa3d68f348951fa410e8c25684ce6c469608711034c880035e74e1f"},"schema_version":"1.0"},"canonical_sha256":"0995aefbcf764b45fe9e3fffe7e6f87b7f710502afc32f4287e323610a4bfc65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:11.268033Z","signature_b64":"ghg+xNJ1051CZA1uVl6V8/jj2N4k6hbKjH2p+h5A2bHtRwOu+GaltP1wwBZj7LCAx7XL3yTBWfTHauHzZo3BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0995aefbcf764b45fe9e3fffe7e6f87b7f710502afc32f4287e323610a4bfc65","last_reissued_at":"2026-05-18T01:37:11.267403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:11.267403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3180","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":"2026-05-18T01:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0DFJPfEpsVyDY9HIUguniUipepW87UkAnO2kV/J44U/LNOUpu48u8XebA6q3oJOFNvp6GEHvoFQLvu6ga7OBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T07:57:53.781270Z"},"content_sha256":"3c19871b70499f169cb75ab94b5c857bc87cbe1146ddeeb102a2f2ba74c8cd0f","schema_version":"1.0","event_id":"sha256:3c19871b70499f169cb75ab94b5c857bc87cbe1146ddeeb102a2f2ba74c8cd0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BGK2566POZFUL7U6H776PZXYPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Daniele Oriti, Dario Benedetti, Joseph Ben Geloun","submitted_at":"2014-11-12T14:10:22Z","abstract_excerpt":"We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3180","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":""},"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":"2026-05-18T01:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MPZGuZvJdlI+3EYU96xk2c0GWoAXptt09DCs4wxYyjhiyRdNcghSP9GbGno2Dvxox1fXQw53g2hTCdwyNLufCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T07:57:53.782075Z"},"content_sha256":"54a1312f0faa1aaf9e5a327445559e55692f002a5f0615700f231930d130733a","schema_version":"1.0","event_id":"sha256:54a1312f0faa1aaf9e5a327445559e55692f002a5f0615700f231930d130733a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGK2566POZFUL7U6H776PZXYPN/bundle.json","state_url":"https://pith.science/pith/BGK2566POZFUL7U6H776PZXYPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGK2566POZFUL7U6H776PZXYPN/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":"2026-06-08T07:57:53Z","links":{"resolver":"https://pith.science/pith/BGK2566POZFUL7U6H776PZXYPN","bundle":"https://pith.science/pith/BGK2566POZFUL7U6H776PZXYPN/bundle.json","state":"https://pith.science/pith/BGK2566POZFUL7U6H776PZXYPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGK2566POZFUL7U6H776PZXYPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BGK2566POZFUL7U6H776PZXYPN","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":"e38a7d065fa3d68f348951fa410e8c25684ce6c469608711034c880035e74e1f","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T14:10:22Z","title_canon_sha256":"b0a7caf5fed72bb68a3e85280a2ae1ad417d263e46fde7ddf842ed42cc8cbbf9"},"schema_version":"1.0","source":{"id":"1411.3180","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3180","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3180v2","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3180","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"BGK2566POZFU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BGK2566POZFUL7U6","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BGK2566P","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:54a1312f0faa1aaf9e5a327445559e55692f002a5f0615700f231930d130733a","target":"graph","created_at":"2026-05-18T01:37:11Z","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"},"paper":{"abstract_excerpt":"We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian a","authors_text":"Daniele Oriti, Dario Benedetti, Joseph Ben Geloun","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T14:10:22Z","title":"Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3180","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":"sha256:3c19871b70499f169cb75ab94b5c857bc87cbe1146ddeeb102a2f2ba74c8cd0f","target":"record","created_at":"2026-05-18T01:37:11Z","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":"e38a7d065fa3d68f348951fa410e8c25684ce6c469608711034c880035e74e1f","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-11-12T14:10:22Z","title_canon_sha256":"b0a7caf5fed72bb68a3e85280a2ae1ad417d263e46fde7ddf842ed42cc8cbbf9"},"schema_version":"1.0","source":{"id":"1411.3180","kind":"arxiv","version":2}},"canonical_sha256":"0995aefbcf764b45fe9e3fffe7e6f87b7f710502afc32f4287e323610a4bfc65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0995aefbcf764b45fe9e3fffe7e6f87b7f710502afc32f4287e323610a4bfc65","first_computed_at":"2026-05-18T01:37:11.267403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:11.267403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ghg+xNJ1051CZA1uVl6V8/jj2N4k6hbKjH2p+h5A2bHtRwOu+GaltP1wwBZj7LCAx7XL3yTBWfTHauHzZo3BDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:11.268033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3180","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c19871b70499f169cb75ab94b5c857bc87cbe1146ddeeb102a2f2ba74c8cd0f","sha256:54a1312f0faa1aaf9e5a327445559e55692f002a5f0615700f231930d130733a"],"state_sha256":"f1ad56e423a7dd9cd75c875c0008cda3fb790ee36a873d8f5f161b97cc3450c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8M0np8wAsc2hLqb1he2raY3NpvvCYfIBokT8MZqOjdOisIRyMtKaQ+3AxEaiAwccUKeXcoM4Xem3m4e25G6HCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T07:57:53.786417Z","bundle_sha256":"87ed54a71116bf33dbd31ac22878e0d765caa55c264878a721633b2989d18b33"}}