{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QNHEGJWRYBUNWJUXWTPMFJC5SY","short_pith_number":"pith:QNHEGJWR","canonical_record":{"source":{"id":"1304.2666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-09T17:08:55Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"5963275491e4299bb39a7f9888ca0023662d69ad18a6e23251334e7f6ac8a440","abstract_canon_sha256":"aa4cdafdaee0008b40101d0283d43691d40f768cd5e420a3073b29de4aaed19e"},"schema_version":"1.0"},"canonical_sha256":"834e4326d1c068db2697b4dec2a45d9635dc9c20708ea7a83350acc0a23df4b5","source":{"kind":"arxiv","id":"1304.2666","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2666","created_at":"2026-05-18T01:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2666v1","created_at":"2026-05-18T01:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2666","created_at":"2026-05-18T01:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"QNHEGJWRYBUN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QNHEGJWRYBUNWJUX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QNHEGJWR","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QNHEGJWRYBUNWJUXWTPMFJC5SY","target":"record","payload":{"canonical_record":{"source":{"id":"1304.2666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-09T17:08:55Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"5963275491e4299bb39a7f9888ca0023662d69ad18a6e23251334e7f6ac8a440","abstract_canon_sha256":"aa4cdafdaee0008b40101d0283d43691d40f768cd5e420a3073b29de4aaed19e"},"schema_version":"1.0"},"canonical_sha256":"834e4326d1c068db2697b4dec2a45d9635dc9c20708ea7a83350acc0a23df4b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:41.002044Z","signature_b64":"DaSkA9Aal+CS7AdwSLsVAhff0/c28/s8cVFb6RN7yUaXVUAJMM/3ujGvEVNYy0XYwYrAUPeK/aUnv8wOmm8eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"834e4326d1c068db2697b4dec2a45d9635dc9c20708ea7a83350acc0a23df4b5","last_reissued_at":"2026-05-18T01:50:41.001386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:41.001386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.2666","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sH6OCQP/bTdM/DiKpyq23esTLLhf64zR/B/YjE2oHAaTaCVY8+121BTY6OmScA2v2S8CdTzWnUaMqf/Xt6uQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:57:46.260244Z"},"content_sha256":"2dc790edb1d5355fb4bb224af9b8ba2434fbeb5d34aaf84fa276f3a042b3db1e","schema_version":"1.0","event_id":"sha256:2dc790edb1d5355fb4bb224af9b8ba2434fbeb5d34aaf84fa276f3a042b3db1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QNHEGJWRYBUNWJUXWTPMFJC5SY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 1/N Expansion of Tensor Models Beyond Perturbation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Razvan Gurau","submitted_at":"2013-04-09T17:08:55Z","abstract_excerpt":"We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges.\n  As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2666","kind":"arxiv","version":1},"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":"2026-05-18T01:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vqz8kZsykgApC6V2wpjgpsiOWL5GPWdB8igkOa5j94FZT3mldw0s343WXd4RcLi5gDW2Rnulr/HBHlhCVh+ZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:57:46.260869Z"},"content_sha256":"d953692458959a3a272abf83d633b65bfb881f4a9e61eda234ae0ee9f429c85b","schema_version":"1.0","event_id":"sha256:d953692458959a3a272abf83d633b65bfb881f4a9e61eda234ae0ee9f429c85b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY/bundle.json","state_url":"https://pith.science/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY/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":"2026-05-25T17:57:46Z","links":{"resolver":"https://pith.science/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY","bundle":"https://pith.science/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY/bundle.json","state":"https://pith.science/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNHEGJWRYBUNWJUXWTPMFJC5SY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QNHEGJWRYBUNWJUXWTPMFJC5SY","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":"aa4cdafdaee0008b40101d0283d43691d40f768cd5e420a3073b29de4aaed19e","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-09T17:08:55Z","title_canon_sha256":"5963275491e4299bb39a7f9888ca0023662d69ad18a6e23251334e7f6ac8a440"},"schema_version":"1.0","source":{"id":"1304.2666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2666","created_at":"2026-05-18T01:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2666v1","created_at":"2026-05-18T01:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2666","created_at":"2026-05-18T01:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"QNHEGJWRYBUN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QNHEGJWRYBUNWJUX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QNHEGJWR","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:d953692458959a3a272abf83d633b65bfb881f4a9e61eda234ae0ee9f429c85b","target":"graph","created_at":"2026-05-18T01:50:41Z","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 analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges.\n  As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Bo","authors_text":"Razvan Gurau","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-09T17:08:55Z","title":"The 1/N Expansion of Tensor Models Beyond Perturbation Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2666","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":"sha256:2dc790edb1d5355fb4bb224af9b8ba2434fbeb5d34aaf84fa276f3a042b3db1e","target":"record","created_at":"2026-05-18T01:50:41Z","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":"aa4cdafdaee0008b40101d0283d43691d40f768cd5e420a3073b29de4aaed19e","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-09T17:08:55Z","title_canon_sha256":"5963275491e4299bb39a7f9888ca0023662d69ad18a6e23251334e7f6ac8a440"},"schema_version":"1.0","source":{"id":"1304.2666","kind":"arxiv","version":1}},"canonical_sha256":"834e4326d1c068db2697b4dec2a45d9635dc9c20708ea7a83350acc0a23df4b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"834e4326d1c068db2697b4dec2a45d9635dc9c20708ea7a83350acc0a23df4b5","first_computed_at":"2026-05-18T01:50:41.001386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:41.001386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DaSkA9Aal+CS7AdwSLsVAhff0/c28/s8cVFb6RN7yUaXVUAJMM/3ujGvEVNYy0XYwYrAUPeK/aUnv8wOmm8eBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:41.002044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dc790edb1d5355fb4bb224af9b8ba2434fbeb5d34aaf84fa276f3a042b3db1e","sha256:d953692458959a3a272abf83d633b65bfb881f4a9e61eda234ae0ee9f429c85b"],"state_sha256":"e1f7f9c6606d3ec954b3f62c77873e227f207fc54af46b582c810b630a4317cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Q4+M2QcwD5ihalWw9JED73HQa3GHANwaw1NqcgjTBKFp5yRiN/S7IF1zwQzfLWAmHghlo/4Yp5MDXi65+0qDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:57:46.264678Z","bundle_sha256":"2dedaeb46b23c80f56496963392d4ce5ae05203a0a1b48895a5eee871b93672f"}}