{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4KD43I7IGUNZVRI4WUVY5GIKXZ","short_pith_number":"pith:4KD43I7I","canonical_record":{"source":{"id":"1304.5977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T15:12:04Z","cross_cats_sorted":[],"title_canon_sha256":"52eb1bbb37a059cb0ddcbd94909c926665dda29f5ca4332bfa9625a468028b98","abstract_canon_sha256":"601a6c97e073b446cc8e9e46475f8624cb56838847009bbf13dcc33c3f07c091"},"schema_version":"1.0"},"canonical_sha256":"e287cda3e8351b9ac51cb52b8e990abe5ea68c01c8c0d1c8eed7dd06002c308c","source":{"kind":"arxiv","id":"1304.5977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5977","created_at":"2026-05-18T03:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5977v1","created_at":"2026-05-18T03:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5977","created_at":"2026-05-18T03:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"4KD43I7IGUNZ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4KD43I7IGUNZVRI4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4KD43I7I","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4KD43I7IGUNZVRI4WUVY5GIKXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T15:12:04Z","cross_cats_sorted":[],"title_canon_sha256":"52eb1bbb37a059cb0ddcbd94909c926665dda29f5ca4332bfa9625a468028b98","abstract_canon_sha256":"601a6c97e073b446cc8e9e46475f8624cb56838847009bbf13dcc33c3f07c091"},"schema_version":"1.0"},"canonical_sha256":"e287cda3e8351b9ac51cb52b8e990abe5ea68c01c8c0d1c8eed7dd06002c308c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:57.540375Z","signature_b64":"UinmChHn6qyo7C67XvWPLedi5KKt8L9cC9I5dqxY76GpCPTRinu2J+8aPGD6ZuWpsb5ffpSlHDgluHjIe5ACDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e287cda3e8351b9ac51cb52b8e990abe5ea68c01c8c0d1c8eed7dd06002c308c","last_reissued_at":"2026-05-18T03:11:57.539769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:57.539769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5977","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":"2026-05-18T03:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4VvsZW303sGg6byxpofR5KOXbOAZNGWbRn75KlM/ItDf4Z+WhRZWPCvMkCIfYRJ9taJiVmA/BPQWqwChYxJxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:57:45.195895Z"},"content_sha256":"aa69daed2cb3099541d0d2426ef37b1748c6d1f2ef065d0ec0936e8df93df819","schema_version":"1.0","event_id":"sha256:aa69daed2cb3099541d0d2426ef37b1748c6d1f2ef065d0ec0936e8df93df819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4KD43I7IGUNZVRI4WUVY5GIKXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general framework for phase and interference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andrew J. P. Garner, Mio Murao, Oscar C. O. Dahlsten, Vlatko Vedral, Yoshifumi Nakata","submitted_at":"2013-04-22T15:12:04Z","abstract_excerpt":"Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalised probabilistic theories, or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5977","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":"2026-05-18T03:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XeBe6W5x8MQ0YyWLEQ0chbvlWZAZd/Q1tY+Kab5jtkRhP3Oz+n6NXWerdLxJ9nCNHXKOC5XxsSUzhNds/ATBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:57:45.196242Z"},"content_sha256":"7ff1e35d79190d9c58639c796e76badfb53bf0ba879eb5bcb4e284b8bb2c5885","schema_version":"1.0","event_id":"sha256:7ff1e35d79190d9c58639c796e76badfb53bf0ba879eb5bcb4e284b8bb2c5885"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ/bundle.json","state_url":"https://pith.science/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ/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":"2026-06-01T05:57:45Z","links":{"resolver":"https://pith.science/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ","bundle":"https://pith.science/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ/bundle.json","state":"https://pith.science/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KD43I7IGUNZVRI4WUVY5GIKXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4KD43I7IGUNZVRI4WUVY5GIKXZ","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":"601a6c97e073b446cc8e9e46475f8624cb56838847009bbf13dcc33c3f07c091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T15:12:04Z","title_canon_sha256":"52eb1bbb37a059cb0ddcbd94909c926665dda29f5ca4332bfa9625a468028b98"},"schema_version":"1.0","source":{"id":"1304.5977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5977","created_at":"2026-05-18T03:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5977v1","created_at":"2026-05-18T03:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5977","created_at":"2026-05-18T03:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"4KD43I7IGUNZ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4KD43I7IGUNZVRI4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4KD43I7I","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:7ff1e35d79190d9c58639c796e76badfb53bf0ba879eb5bcb4e284b8bb2c5885","target":"graph","created_at":"2026-05-18T03:11:57Z","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":"Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalised probabilistic theories, or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference ","authors_text":"Andrew J. P. Garner, Mio Murao, Oscar C. O. Dahlsten, Vlatko Vedral, Yoshifumi Nakata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T15:12:04Z","title":"A general framework for phase and interference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5977","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:aa69daed2cb3099541d0d2426ef37b1748c6d1f2ef065d0ec0936e8df93df819","target":"record","created_at":"2026-05-18T03:11:57Z","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":"601a6c97e073b446cc8e9e46475f8624cb56838847009bbf13dcc33c3f07c091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T15:12:04Z","title_canon_sha256":"52eb1bbb37a059cb0ddcbd94909c926665dda29f5ca4332bfa9625a468028b98"},"schema_version":"1.0","source":{"id":"1304.5977","kind":"arxiv","version":1}},"canonical_sha256":"e287cda3e8351b9ac51cb52b8e990abe5ea68c01c8c0d1c8eed7dd06002c308c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e287cda3e8351b9ac51cb52b8e990abe5ea68c01c8c0d1c8eed7dd06002c308c","first_computed_at":"2026-05-18T03:11:57.539769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:57.539769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UinmChHn6qyo7C67XvWPLedi5KKt8L9cC9I5dqxY76GpCPTRinu2J+8aPGD6ZuWpsb5ffpSlHDgluHjIe5ACDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:57.540375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa69daed2cb3099541d0d2426ef37b1748c6d1f2ef065d0ec0936e8df93df819","sha256:7ff1e35d79190d9c58639c796e76badfb53bf0ba879eb5bcb4e284b8bb2c5885"],"state_sha256":"999a7c90acb17ce9c88b51ed0f38f7b58ffa08ac8bf85de35a24bfec58427c14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbbFcLzH+hJ8ki8SskwuqWectL3WR77mUUvDZnXNvor78WQMCg/ESMCNxm/E0tJnmtCn+C7y3ztsYXTIVnPiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:57:45.201485Z","bundle_sha256":"c36026378a34d4d7199b43352261d7595301ca40f776dfc0fd86ff74a4eb06f3"}}