{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7AMUIGOFMQ6V67CQ56EPDBKCNL","short_pith_number":"pith:7AMUIGOF","canonical_record":{"source":{"id":"1706.06070","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-19T17:28:27Z","cross_cats_sorted":["hep-th","math.MP","math.OA"],"title_canon_sha256":"aba4c2c6920d72a71de8054fde6d10f2ca57935762be394ebc19e553495fd1bc","abstract_canon_sha256":"bbff29b1c19207eddcd694827bd982086bb506127488309e0f30329f2a796057"},"schema_version":"1.0"},"canonical_sha256":"f8194419c5643d5f7c50ef88f185426ad29248ae4792f66daa810cb0e43a73c1","source":{"kind":"arxiv","id":"1706.06070","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06070","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06070v1","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06070","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"7AMUIGOFMQ6V","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7AMUIGOFMQ6V67CQ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7AMUIGOF","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7AMUIGOFMQ6V67CQ56EPDBKCNL","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06070","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-19T17:28:27Z","cross_cats_sorted":["hep-th","math.MP","math.OA"],"title_canon_sha256":"aba4c2c6920d72a71de8054fde6d10f2ca57935762be394ebc19e553495fd1bc","abstract_canon_sha256":"bbff29b1c19207eddcd694827bd982086bb506127488309e0f30329f2a796057"},"schema_version":"1.0"},"canonical_sha256":"f8194419c5643d5f7c50ef88f185426ad29248ae4792f66daa810cb0e43a73c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:08.181826Z","signature_b64":"M9LYey4vx30uKWQgSWoh6NhJ9hGN5Gv5mfYRuY4VU8FY/Jl3JDXi6b9ois70IvZ8+H3hIS951Obx03wbem+kBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8194419c5643d5f7c50ef88f185426ad29248ae4792f66daa810cb0e43a73c1","last_reissued_at":"2026-05-18T00:42:08.181450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:08.181450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06070","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":"2026-05-18T00:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWFLqH7jW+BTaGYGbLXKfMdylJQDSXKLezOZiIO8eILNGBSOFVlzjTZlMoC647y4snJdr4AWIr0qKKsn9N/JBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:53:45.948772Z"},"content_sha256":"d5acd3669fc47a410ceaa28f0f796450e4ca9c17dc47da5f5084b44e79f8256f","schema_version":"1.0","event_id":"sha256:d5acd3669fc47a410ceaa28f0f796450e4ca9c17dc47da5f5084b44e79f8256f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7AMUIGOFMQ6V67CQ56EPDBKCNL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free products in AQFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Roberto Longo, Yoh Tanimoto, Yoshimichi Ueda","submitted_at":"2017-06-19T17:28:27Z","abstract_excerpt":"We apply the free product construction to various local algebras in algebraic quantum field theory.\n  If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a half-sided modular inclusion with ergodic canonical endomorphism and trivial relative commutant. On the other hand, if we take M\\\"obius covariant nets with trace class property, we are able to construct an inclusion of free product von Neumann algebras with large relative commutant, by considering either a finite family of identical inclusions or an infinite f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06070","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":"2026-05-18T00:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HY9DZUWpdTTMr2iLMRB6O81dwHyQGjamjExHAHbChYX2YEGhvGO+D8cWaACPODY4MIZ9rWGseL3ns/hpspFACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:53:45.949353Z"},"content_sha256":"c8cd22ae40189018d5d2bf0aa65a46e12fc3284a5b943e2a93bc2dce9becf540","schema_version":"1.0","event_id":"sha256:c8cd22ae40189018d5d2bf0aa65a46e12fc3284a5b943e2a93bc2dce9becf540"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL/bundle.json","state_url":"https://pith.science/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL/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":"2026-05-23T01:53:45Z","links":{"resolver":"https://pith.science/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL","bundle":"https://pith.science/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL/bundle.json","state":"https://pith.science/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AMUIGOFMQ6V67CQ56EPDBKCNL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7AMUIGOFMQ6V67CQ56EPDBKCNL","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":"bbff29b1c19207eddcd694827bd982086bb506127488309e0f30329f2a796057","cross_cats_sorted":["hep-th","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-19T17:28:27Z","title_canon_sha256":"aba4c2c6920d72a71de8054fde6d10f2ca57935762be394ebc19e553495fd1bc"},"schema_version":"1.0","source":{"id":"1706.06070","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06070","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06070v1","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06070","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"7AMUIGOFMQ6V","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7AMUIGOFMQ6V67CQ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7AMUIGOF","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:c8cd22ae40189018d5d2bf0aa65a46e12fc3284a5b943e2a93bc2dce9becf540","target":"graph","created_at":"2026-05-18T00:42:08Z","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 apply the free product construction to various local algebras in algebraic quantum field theory.\n  If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a half-sided modular inclusion with ergodic canonical endomorphism and trivial relative commutant. On the other hand, if we take M\\\"obius covariant nets with trace class property, we are able to construct an inclusion of free product von Neumann algebras with large relative commutant, by considering either a finite family of identical inclusions or an infinite f","authors_text":"Roberto Longo, Yoh Tanimoto, Yoshimichi Ueda","cross_cats":["hep-th","math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-19T17:28:27Z","title":"Free products in AQFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06070","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:d5acd3669fc47a410ceaa28f0f796450e4ca9c17dc47da5f5084b44e79f8256f","target":"record","created_at":"2026-05-18T00:42:08Z","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":"bbff29b1c19207eddcd694827bd982086bb506127488309e0f30329f2a796057","cross_cats_sorted":["hep-th","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-19T17:28:27Z","title_canon_sha256":"aba4c2c6920d72a71de8054fde6d10f2ca57935762be394ebc19e553495fd1bc"},"schema_version":"1.0","source":{"id":"1706.06070","kind":"arxiv","version":1}},"canonical_sha256":"f8194419c5643d5f7c50ef88f185426ad29248ae4792f66daa810cb0e43a73c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8194419c5643d5f7c50ef88f185426ad29248ae4792f66daa810cb0e43a73c1","first_computed_at":"2026-05-18T00:42:08.181450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:08.181450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9LYey4vx30uKWQgSWoh6NhJ9hGN5Gv5mfYRuY4VU8FY/Jl3JDXi6b9ois70IvZ8+H3hIS951Obx03wbem+kBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:08.181826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06070","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5acd3669fc47a410ceaa28f0f796450e4ca9c17dc47da5f5084b44e79f8256f","sha256:c8cd22ae40189018d5d2bf0aa65a46e12fc3284a5b943e2a93bc2dce9becf540"],"state_sha256":"3b27e20deac3455752a410c205d70b0738f90e21070b5295a8edc58407328433"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w93f4UGGFFgS1Qu/FwcQttGM1cOraqEwmPtEXafOct50Vd3kxWlW1bGK05kSyhwH5FOuX6cfpNitfIHdDuuECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T01:53:45.952198Z","bundle_sha256":"4844f516b4ef805d4b17c7d958273f27dcfc6d58d49a6327cf5ef6d99541147a"}}