{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:BBRYVWUX7FVD4ZSG55RSFWKE5H","short_pith_number":"pith:BBRYVWUX","canonical_record":{"source":{"id":"0710.0223","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-10-01T08:07:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a2df4eef14535c3c8859f8971188fe8708d4430142bb25d0eff4086bce029f1a","abstract_canon_sha256":"37aed141808f8b07135d26fee5e42dce9aa2d008de6caf44b6d559d14af1a465"},"schema_version":"1.0"},"canonical_sha256":"08638ada97f96a3e6646ef6322d944e9d4a758fd2400ee298af7ed01bb1d9675","source":{"kind":"arxiv","id":"0710.0223","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0223","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0223v2","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0223","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"BBRYVWUX7FVD","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"pith_short_16","alias_value":"BBRYVWUX7FVD4ZSG","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"pith_short_8","alias_value":"BBRYVWUX","created_at":"2026-07-04T17:05:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:BBRYVWUX7FVD4ZSG55RSFWKE5H","target":"record","payload":{"canonical_record":{"source":{"id":"0710.0223","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-10-01T08:07:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a2df4eef14535c3c8859f8971188fe8708d4430142bb25d0eff4086bce029f1a","abstract_canon_sha256":"37aed141808f8b07135d26fee5e42dce9aa2d008de6caf44b6d559d14af1a465"},"schema_version":"1.0"},"canonical_sha256":"08638ada97f96a3e6646ef6322d944e9d4a758fd2400ee298af7ed01bb1d9675","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:05:56.495771Z","signature_b64":"7qHOC7apuroIgE3uInYGyaZrW77Chu2xseaA02mstEyYRNK9G3A09gDpJQKy/EyL8r78QmdrppY7O/YuLw8ABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08638ada97f96a3e6646ef6322d944e9d4a758fd2400ee298af7ed01bb1d9675","last_reissued_at":"2026-07-04T17:05:56.495432Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:05:56.495432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.0223","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":"2026-07-04T17:05:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32vVxjR88sDw1Q7qJO5JwvXuiphv5IdzuM+LNf1YF7sbMfvYmfywkBNUCRVtqk/wzP3qkmo3OxMWXUO61ws0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T06:05:55.248476Z"},"content_sha256":"e80d0683b253992266ad7285598dbf3f20e3f9743a7c35bb2feb84b6dd3f0c50","schema_version":"1.0","event_id":"sha256:e80d0683b253992266ad7285598dbf3f20e3f9743a7c35bb2feb84b6dd3f0c50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:BBRYVWUX7FVD4ZSG55RSFWKE5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological expansion and boundary conditions","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Bertrand Eynard (SPhT), Nicolas Orantin (SPhT)","submitted_at":"2007-10-01T08:07:30Z","abstract_excerpt":"In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0223","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/0710.0223/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":"2026-07-04T17:05:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+0LUHwY9Yxj/Hw9hqR/R5xIihhAEO/G6akCFm9K+e3oscSk2SN1OqYVL6loD0t7ZELD/jtGrsfIcnh/CCByBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T06:05:55.249159Z"},"content_sha256":"62e227f26acc193d017e46c56b82b86f7faccc85a1966c1bcbefdc0c2f520a7c","schema_version":"1.0","event_id":"sha256:62e227f26acc193d017e46c56b82b86f7faccc85a1966c1bcbefdc0c2f520a7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H/bundle.json","state_url":"https://pith.science/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H/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":"2026-08-19T06:05:55Z","links":{"resolver":"https://pith.science/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H","bundle":"https://pith.science/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H/bundle.json","state":"https://pith.science/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBRYVWUX7FVD4ZSG55RSFWKE5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BBRYVWUX7FVD4ZSG55RSFWKE5H","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":"37aed141808f8b07135d26fee5e42dce9aa2d008de6caf44b6d559d14af1a465","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2007-10-01T08:07:30Z","title_canon_sha256":"a2df4eef14535c3c8859f8971188fe8708d4430142bb25d0eff4086bce029f1a"},"schema_version":"1.0","source":{"id":"0710.0223","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.0223","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"0710.0223v2","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0223","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"BBRYVWUX7FVD","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"pith_short_16","alias_value":"BBRYVWUX7FVD4ZSG","created_at":"2026-07-04T17:05:56Z"},{"alias_kind":"pith_short_8","alias_value":"BBRYVWUX","created_at":"2026-07-04T17:05:56Z"}],"graph_snapshots":[{"event_id":"sha256:62e227f26acc193d017e46c56b82b86f7faccc85a1966c1bcbefdc0c2f520a7c","target":"graph","created_at":"2026-07-04T17:05:56Z","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/0710.0223/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.","authors_text":"Bertrand Eynard (SPhT), Nicolas Orantin (SPhT)","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-10-01T08:07:30Z","title":"Topological expansion and boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0223","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:e80d0683b253992266ad7285598dbf3f20e3f9743a7c35bb2feb84b6dd3f0c50","target":"record","created_at":"2026-07-04T17:05:56Z","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":"37aed141808f8b07135d26fee5e42dce9aa2d008de6caf44b6d559d14af1a465","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2007-10-01T08:07:30Z","title_canon_sha256":"a2df4eef14535c3c8859f8971188fe8708d4430142bb25d0eff4086bce029f1a"},"schema_version":"1.0","source":{"id":"0710.0223","kind":"arxiv","version":2}},"canonical_sha256":"08638ada97f96a3e6646ef6322d944e9d4a758fd2400ee298af7ed01bb1d9675","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08638ada97f96a3e6646ef6322d944e9d4a758fd2400ee298af7ed01bb1d9675","first_computed_at":"2026-07-04T17:05:56.495432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:05:56.495432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7qHOC7apuroIgE3uInYGyaZrW77Chu2xseaA02mstEyYRNK9G3A09gDpJQKy/EyL8r78QmdrppY7O/YuLw8ABA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:05:56.495771Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.0223","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e80d0683b253992266ad7285598dbf3f20e3f9743a7c35bb2feb84b6dd3f0c50","sha256:62e227f26acc193d017e46c56b82b86f7faccc85a1966c1bcbefdc0c2f520a7c"],"state_sha256":"935d94f88d8f9ae150ab6f54aabb05c70388f7498041bfeded13ed40a8ab272a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGskJxqzCNKyd+rpmwsBSL+DLPJSs3hojfhrAVZQAsgZar+ZwJrCXapaEMISoAzIBiL66NgeNshvwXI2Y6EeBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T06:05:55.254918Z","bundle_sha256":"aa90477b77cfadabff95b5fab7819a07193c6905996d51c03692a9cfdecaf1eb"}}