{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZRQ6P47JFLT773WOPDYP2MGJXR","short_pith_number":"pith:ZRQ6P47J","canonical_record":{"source":{"id":"1907.03531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-07-08T11:59:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ee5ead1e7866efb4efc61b09a56fad085f21e62a346fba9d3ce0521985e4afd3","abstract_canon_sha256":"fc9a25a753af1e80ebaf57d7e3d629dd2f1bae92797a004a9169ece546e6bd2f"},"schema_version":"1.0"},"canonical_sha256":"cc61e7f3e92ae7ffeece78f0fd30c9bc6f544c7420fe02e00befcd9431e41d7f","source":{"kind":"arxiv","id":"1907.03531","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03531","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03531v2","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03531","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZRQ6P47JFLT7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZRQ6P47JFLT773WO","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZRQ6P47J","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZRQ6P47JFLT773WOPDYP2MGJXR","target":"record","payload":{"canonical_record":{"source":{"id":"1907.03531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-07-08T11:59:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ee5ead1e7866efb4efc61b09a56fad085f21e62a346fba9d3ce0521985e4afd3","abstract_canon_sha256":"fc9a25a753af1e80ebaf57d7e3d629dd2f1bae92797a004a9169ece546e6bd2f"},"schema_version":"1.0"},"canonical_sha256":"cc61e7f3e92ae7ffeece78f0fd30c9bc6f544c7420fe02e00befcd9431e41d7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:38.533580Z","signature_b64":"IU8+VZZaPo+AGAS1zFG7ct0z3XbhEXr0Q0JvsA00eMPDeYi7YN1Ly86MwkoIo4/mnPtGshFUM/pkZCE8IFY+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc61e7f3e92ae7ffeece78f0fd30c9bc6f544c7420fe02e00befcd9431e41d7f","last_reissued_at":"2026-05-17T23:40:38.532958Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:38.532958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.03531","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":"2026-05-17T23:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqQKZaIYOCNyvOEYhF6NUPsXxYksOZ4CbxEFSEqhJR+vHSeZ66KoiRiX9S+4nJ3iAeQ29CjO4nHIzvLhnG8mDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:46:07.663299Z"},"content_sha256":"60041ecaef2a4e76fe9872c10b90fa1462d1bb64be11fc8fb0be30cb9d2cb512","schema_version":"1.0","event_id":"sha256:60041ecaef2a4e76fe9872c10b90fa1462d1bb64be11fc8fb0be30cb9d2cb512"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZRQ6P47JFLT773WOPDYP2MGJXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on Tensor Models and Tensor Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Razvan Gurau","submitted_at":"2019-07-08T11:59:43Z","abstract_excerpt":"Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of analytically tractable but non trivial strongly coupled quantum field theories and lead to a new class of conformal field theories. We present a compact introduction to the topic, covering both some of the classical results in the field, like the details of the $1/N$ expansion, as well as recent developments. These notes are loosely bases on four lectures given at th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03531","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":"2026-05-17T23:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uw6xfxJsd71Ig/3MSwHPns2aMcXLI9aQPr1DSOZSsGqHkjoZ5CzpQJ+87CkObOdPVWHGrA8K8sEOVV1Aa6dMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:46:07.663729Z"},"content_sha256":"17cda2ed0bd8418191741252b07801b0ff6641a9ceb5d799c02a7d0f54afcad5","schema_version":"1.0","event_id":"sha256:17cda2ed0bd8418191741252b07801b0ff6641a9ceb5d799c02a7d0f54afcad5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZRQ6P47JFLT773WOPDYP2MGJXR/bundle.json","state_url":"https://pith.science/pith/ZRQ6P47JFLT773WOPDYP2MGJXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZRQ6P47JFLT773WOPDYP2MGJXR/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":"2026-05-25T20:46:07Z","links":{"resolver":"https://pith.science/pith/ZRQ6P47JFLT773WOPDYP2MGJXR","bundle":"https://pith.science/pith/ZRQ6P47JFLT773WOPDYP2MGJXR/bundle.json","state":"https://pith.science/pith/ZRQ6P47JFLT773WOPDYP2MGJXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZRQ6P47JFLT773WOPDYP2MGJXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZRQ6P47JFLT773WOPDYP2MGJXR","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":"fc9a25a753af1e80ebaf57d7e3d629dd2f1bae92797a004a9169ece546e6bd2f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-07-08T11:59:43Z","title_canon_sha256":"ee5ead1e7866efb4efc61b09a56fad085f21e62a346fba9d3ce0521985e4afd3"},"schema_version":"1.0","source":{"id":"1907.03531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03531","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03531v2","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03531","created_at":"2026-05-17T23:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZRQ6P47JFLT7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZRQ6P47JFLT773WO","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZRQ6P47J","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:17cda2ed0bd8418191741252b07801b0ff6641a9ceb5d799c02a7d0f54afcad5","target":"graph","created_at":"2026-05-17T23:40:38Z","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":"Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of analytically tractable but non trivial strongly coupled quantum field theories and lead to a new class of conformal field theories. We present a compact introduction to the topic, covering both some of the classical results in the field, like the details of the $1/N$ expansion, as well as recent developments. These notes are loosely bases on four lectures given at th","authors_text":"Razvan Gurau","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-07-08T11:59:43Z","title":"Notes on Tensor Models and Tensor Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03531","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":"sha256:60041ecaef2a4e76fe9872c10b90fa1462d1bb64be11fc8fb0be30cb9d2cb512","target":"record","created_at":"2026-05-17T23:40:38Z","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":"fc9a25a753af1e80ebaf57d7e3d629dd2f1bae92797a004a9169ece546e6bd2f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-07-08T11:59:43Z","title_canon_sha256":"ee5ead1e7866efb4efc61b09a56fad085f21e62a346fba9d3ce0521985e4afd3"},"schema_version":"1.0","source":{"id":"1907.03531","kind":"arxiv","version":2}},"canonical_sha256":"cc61e7f3e92ae7ffeece78f0fd30c9bc6f544c7420fe02e00befcd9431e41d7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc61e7f3e92ae7ffeece78f0fd30c9bc6f544c7420fe02e00befcd9431e41d7f","first_computed_at":"2026-05-17T23:40:38.532958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:38.532958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IU8+VZZaPo+AGAS1zFG7ct0z3XbhEXr0Q0JvsA00eMPDeYi7YN1Ly86MwkoIo4/mnPtGshFUM/pkZCE8IFY+Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:38.533580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60041ecaef2a4e76fe9872c10b90fa1462d1bb64be11fc8fb0be30cb9d2cb512","sha256:17cda2ed0bd8418191741252b07801b0ff6641a9ceb5d799c02a7d0f54afcad5"],"state_sha256":"7bfa900bdf8805f45c71f7833dc453297dfbfce6ee5975480cead80c2c40accf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5gfC53jsPq4ugeU+OyzHOLhs4NDbiSgdtMwEzaV/KEKvIoKjxV9y7VN5vxnKRhLIMQsef1R3LX7ktTNa6BWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:46:07.666055Z","bundle_sha256":"51edd2dcecedcf0a4515ca450e4a5cdeae732d492f92f0384d68cc20fd555ad7"}}