{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EBZRFXHB2AAJ2ACPPC7A3GDXOA","short_pith_number":"pith:EBZRFXHB","canonical_record":{"source":{"id":"1803.02496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-07T01:32:38Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"d63dbf3213baa3ca4d2202f81bbafc40909dea1dd2eecf0bbdfdaba532606169","abstract_canon_sha256":"c1a008d11bfe85207aadc7ac5d4cd0f03b6cb1ec1851c0f1bab825b401f22b11"},"schema_version":"1.0"},"canonical_sha256":"207312dce1d0009d004f78be0d9877702b3efdca84c917a8051a448578397ca7","source":{"kind":"arxiv","id":"1803.02496","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02496","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02496v2","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02496","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"pith_short_12","alias_value":"EBZRFXHB2AAJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EBZRFXHB2AAJ2ACP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EBZRFXHB","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EBZRFXHB2AAJ2ACPPC7A3GDXOA","target":"record","payload":{"canonical_record":{"source":{"id":"1803.02496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-07T01:32:38Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"d63dbf3213baa3ca4d2202f81bbafc40909dea1dd2eecf0bbdfdaba532606169","abstract_canon_sha256":"c1a008d11bfe85207aadc7ac5d4cd0f03b6cb1ec1851c0f1bab825b401f22b11"},"schema_version":"1.0"},"canonical_sha256":"207312dce1d0009d004f78be0d9877702b3efdca84c917a8051a448578397ca7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:50.686778Z","signature_b64":"5q78m1F/4+SARLKbaRxygYRhUVeV0indTxzIgexSKZD6M0mSTliambxpn5hnU1pt8fcSfIvWLoO9D6zwDWGHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"207312dce1d0009d004f78be0d9877702b3efdca84c917a8051a448578397ca7","last_reissued_at":"2026-05-18T00:13:50.684938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:50.684938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.02496","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":"2026-05-18T00:13:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bwBQJd62gTJ9EX5gqf8spu/rUOVxFzpwmROhvxbvdnjtFYb652PX2KrPNFoE1ypITYWAVndoWa8Dq7IGcyfiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:38:35.705638Z"},"content_sha256":"9f47b06df6211dcd05e0ba14496b6cb09bfc59825efc3d90df7f1413206ff8e2","schema_version":"1.0","event_id":"sha256:9f47b06df6211dcd05e0ba14496b6cb09bfc59825efc3d90df7f1413206ff8e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EBZRFXHB2AAJ2ACPPC7A3GDXOA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Sylvain Carrozza","submitted_at":"2018-03-07T01:32:38Z","abstract_excerpt":"It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results to the last irreducible $O(N)$ tensor representation available in this context, which carries a two-dimensional representation of the symmetric group $S_3$. Along the way, we emphasize the role of the irreducibility condition: it prevents the generation of vector modes which are not compatible with the large $N$ scaling of the tensor interaction. This examp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02496","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":"2026-05-18T00:13:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CwoCG+Jqfjcn7DQyjAPbuthzOxYayAKCt77qPR4zybZc5eJx5icu980jYGBybHrDYZmBzEWMvOe5isL3eIDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:38:35.705989Z"},"content_sha256":"883efac41ec5f27f3dea8a0247e3905a61077f95a487eb716039299c0a2e505a","schema_version":"1.0","event_id":"sha256:883efac41ec5f27f3dea8a0247e3905a61077f95a487eb716039299c0a2e505a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA/bundle.json","state_url":"https://pith.science/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA/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":"2026-06-27T16:38:35Z","links":{"resolver":"https://pith.science/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA","bundle":"https://pith.science/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA/bundle.json","state":"https://pith.science/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBZRFXHB2AAJ2ACPPC7A3GDXOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EBZRFXHB2AAJ2ACPPC7A3GDXOA","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":"c1a008d11bfe85207aadc7ac5d4cd0f03b6cb1ec1851c0f1bab825b401f22b11","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-07T01:32:38Z","title_canon_sha256":"d63dbf3213baa3ca4d2202f81bbafc40909dea1dd2eecf0bbdfdaba532606169"},"schema_version":"1.0","source":{"id":"1803.02496","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02496","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02496v2","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02496","created_at":"2026-05-18T00:13:50Z"},{"alias_kind":"pith_short_12","alias_value":"EBZRFXHB2AAJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EBZRFXHB2AAJ2ACP","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EBZRFXHB","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:883efac41ec5f27f3dea8a0247e3905a61077f95a487eb716039299c0a2e505a","target":"graph","created_at":"2026-05-18T00:13:50Z","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":"It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results to the last irreducible $O(N)$ tensor representation available in this context, which carries a two-dimensional representation of the symmetric group $S_3$. Along the way, we emphasize the role of the irreducibility condition: it prevents the generation of vector modes which are not compatible with the large $N$ scaling of the tensor interaction. This examp","authors_text":"Sylvain Carrozza","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-07T01:32:38Z","title":"Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02496","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":"sha256:9f47b06df6211dcd05e0ba14496b6cb09bfc59825efc3d90df7f1413206ff8e2","target":"record","created_at":"2026-05-18T00:13:50Z","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":"c1a008d11bfe85207aadc7ac5d4cd0f03b6cb1ec1851c0f1bab825b401f22b11","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-07T01:32:38Z","title_canon_sha256":"d63dbf3213baa3ca4d2202f81bbafc40909dea1dd2eecf0bbdfdaba532606169"},"schema_version":"1.0","source":{"id":"1803.02496","kind":"arxiv","version":2}},"canonical_sha256":"207312dce1d0009d004f78be0d9877702b3efdca84c917a8051a448578397ca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"207312dce1d0009d004f78be0d9877702b3efdca84c917a8051a448578397ca7","first_computed_at":"2026-05-18T00:13:50.684938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:50.684938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5q78m1F/4+SARLKbaRxygYRhUVeV0indTxzIgexSKZD6M0mSTliambxpn5hnU1pt8fcSfIvWLoO9D6zwDWGHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:50.686778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02496","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f47b06df6211dcd05e0ba14496b6cb09bfc59825efc3d90df7f1413206ff8e2","sha256:883efac41ec5f27f3dea8a0247e3905a61077f95a487eb716039299c0a2e505a"],"state_sha256":"fa2e712e08bc2d154920c9e10827fc3b71aa5c7e62a0f6ef7914dc19fe3acf15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6DygBlZnHOTyZwg4v91xlN3m/nBUnNxRP5CPgjdRdnXtG8nXOGAlQIC81C1j10htJifQqELnZE6Y78j/p+nDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:38:35.707896Z","bundle_sha256":"295f95b01b89d754435edd6cd93c531e817f70aa30763149c19d644df6c59eab"}}