{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XYQXHW2QTRN4L2WJQFVVXUEBW6","short_pith_number":"pith:XYQXHW2Q","canonical_record":{"source":{"id":"1302.2604","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-11T20:34:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3cc27aa23029610abfe2406d9293c3ef0c776b6a57cbc263ebb92746448cd2a6","abstract_canon_sha256":"308a58d29009239aae2b75ac073acf4969aee82206628e241596d8f5f0e02588"},"schema_version":"1.0"},"canonical_sha256":"be2173db509c5bc5eac9816b5bd081b78746152071eb49731a3e4ccc95e8a9d3","source":{"kind":"arxiv","id":"1302.2604","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2604","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2604v3","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2604","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"XYQXHW2QTRN4","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XYQXHW2QTRN4L2WJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XYQXHW2Q","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XYQXHW2QTRN4L2WJQFVVXUEBW6","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2604","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-11T20:34:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3cc27aa23029610abfe2406d9293c3ef0c776b6a57cbc263ebb92746448cd2a6","abstract_canon_sha256":"308a58d29009239aae2b75ac073acf4969aee82206628e241596d8f5f0e02588"},"schema_version":"1.0"},"canonical_sha256":"be2173db509c5bc5eac9816b5bd081b78746152071eb49731a3e4ccc95e8a9d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:29.529863Z","signature_b64":"Hg0d1Y0I8dEAHTchcHohWU9xjxevVuq/Yyel4YPek5CtKTcTJ1y1sy0iEgg1ooB41e28zoTQmjvNBHetm0jkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be2173db509c5bc5eac9816b5bd081b78746152071eb49731a3e4ccc95e8a9d3","last_reissued_at":"2026-05-18T00:52:29.529376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:29.529376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2604","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x7T5NYOzY8UFeq+7ELCD+tq2luDjlbMs1i6JdlVCI0Fjes9LR0HKp8O2olplMg7nFSno6NBge2V2Xtfr3R/9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T01:24:56.201161Z"},"content_sha256":"5d4b66507cb4c62e6b5f1a85c0ebd361486a3cd30a4326e8b9661ce965a628f1","schema_version":"1.0","event_id":"sha256:5d4b66507cb4c62e6b5f1a85c0ebd361486a3cd30a4326e8b9661ce965a628f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XYQXHW2QTRN4L2WJQFVVXUEBW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal nets I: coordinate-free nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Andr\\'e Henriques, Arthur Bartels, Christopher L. Douglas","submitted_at":"2013-02-11T20:34:23Z","abstract_excerpt":"We describe a coordinate-free perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of von Neumann algebras. Though coordinate-free nets do not a priori have vacuum sectors, we show that there is a vacuum sector canonically associated to any circle equipped with a conformal structure. This is the first in a series of papers constructing a 3-category of conformal nets, defects, sectors, and intertwiners."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2604","kind":"arxiv","version":3},"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":"2026-05-18T00:52:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Ic9leIORScCXYQtXtKd4Nt9/PYojVWCXmlOaY/Qke01cH8Q7/tKOeKb6OteXUweBV6T7qoGO+3WsS9X2L7OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T01:24:56.201534Z"},"content_sha256":"1a5230a32beb4a3fea37303195661042b8d13e64a8a55ca7117f7a969fd249c1","schema_version":"1.0","event_id":"sha256:1a5230a32beb4a3fea37303195661042b8d13e64a8a55ca7117f7a969fd249c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6/bundle.json","state_url":"https://pith.science/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6/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":"2026-06-30T01:24:56Z","links":{"resolver":"https://pith.science/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6","bundle":"https://pith.science/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6/bundle.json","state":"https://pith.science/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XYQXHW2QTRN4L2WJQFVVXUEBW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XYQXHW2QTRN4L2WJQFVVXUEBW6","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":"308a58d29009239aae2b75ac073acf4969aee82206628e241596d8f5f0e02588","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-11T20:34:23Z","title_canon_sha256":"3cc27aa23029610abfe2406d9293c3ef0c776b6a57cbc263ebb92746448cd2a6"},"schema_version":"1.0","source":{"id":"1302.2604","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2604","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2604v3","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2604","created_at":"2026-05-18T00:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"XYQXHW2QTRN4","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XYQXHW2QTRN4L2WJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XYQXHW2Q","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:1a5230a32beb4a3fea37303195661042b8d13e64a8a55ca7117f7a969fd249c1","target":"graph","created_at":"2026-05-18T00:52:29Z","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 describe a coordinate-free perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of von Neumann algebras. Though coordinate-free nets do not a priori have vacuum sectors, we show that there is a vacuum sector canonically associated to any circle equipped with a conformal structure. This is the first in a series of papers constructing a 3-category of conformal nets, defects, sectors, and intertwiners.","authors_text":"Andr\\'e Henriques, Arthur Bartels, Christopher L. Douglas","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-11T20:34:23Z","title":"Conformal nets I: coordinate-free nets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2604","kind":"arxiv","version":3},"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":"sha256:5d4b66507cb4c62e6b5f1a85c0ebd361486a3cd30a4326e8b9661ce965a628f1","target":"record","created_at":"2026-05-18T00:52:29Z","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":"308a58d29009239aae2b75ac073acf4969aee82206628e241596d8f5f0e02588","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-11T20:34:23Z","title_canon_sha256":"3cc27aa23029610abfe2406d9293c3ef0c776b6a57cbc263ebb92746448cd2a6"},"schema_version":"1.0","source":{"id":"1302.2604","kind":"arxiv","version":3}},"canonical_sha256":"be2173db509c5bc5eac9816b5bd081b78746152071eb49731a3e4ccc95e8a9d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be2173db509c5bc5eac9816b5bd081b78746152071eb49731a3e4ccc95e8a9d3","first_computed_at":"2026-05-18T00:52:29.529376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:29.529376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hg0d1Y0I8dEAHTchcHohWU9xjxevVuq/Yyel4YPek5CtKTcTJ1y1sy0iEgg1ooB41e28zoTQmjvNBHetm0jkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:29.529863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2604","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d4b66507cb4c62e6b5f1a85c0ebd361486a3cd30a4326e8b9661ce965a628f1","sha256:1a5230a32beb4a3fea37303195661042b8d13e64a8a55ca7117f7a969fd249c1"],"state_sha256":"0f0eb22af6ced094375f7f0d7ed5108dd0c741b9286e9ee440aca7ad6d672bef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UG52qRxOQBWjVHu9GdR+aGuHGYYxkIHRjJ7yciB4/tlWO/ufjIknOSvz21mOBgZ1v1iMOFAKR+QzTTkfafYHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T01:24:56.203518Z","bundle_sha256":"e7f1ff6598afe5a92b99a01a8bdfbc2117fb662852bc58ea008b36e114f23af1"}}