{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:4RZWFXBH5CKIZJZGEADZZLVX7R","short_pith_number":"pith:4RZWFXBH","canonical_record":{"source":{"id":"0711.0112","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-11-01T15:40:37Z","cross_cats_sorted":[],"title_canon_sha256":"30d743a9cabf931764b11dc80e821180247d31418acfa52ac344718bfc99268a","abstract_canon_sha256":"c1258017548624c5ea464481f3ef886763e23bdc70aef870e855c65e9138e5c3"},"schema_version":"1.0"},"canonical_sha256":"e47362dc27e8948ca72620079caeb7fc4086c89e98bf9c7058f365c9bbb1e1ac","source":{"kind":"arxiv","id":"0711.0112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0112","created_at":"2026-05-18T02:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0112v1","created_at":"2026-05-18T02:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0112","created_at":"2026-05-18T02:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"4RZWFXBH5CKI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"4RZWFXBH5CKIZJZG","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"4RZWFXBH","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:4RZWFXBH5CKIZJZGEADZZLVX7R","target":"record","payload":{"canonical_record":{"source":{"id":"0711.0112","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-11-01T15:40:37Z","cross_cats_sorted":[],"title_canon_sha256":"30d743a9cabf931764b11dc80e821180247d31418acfa52ac344718bfc99268a","abstract_canon_sha256":"c1258017548624c5ea464481f3ef886763e23bdc70aef870e855c65e9138e5c3"},"schema_version":"1.0"},"canonical_sha256":"e47362dc27e8948ca72620079caeb7fc4086c89e98bf9c7058f365c9bbb1e1ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:09.858854Z","signature_b64":"zGVf++CEtNW8zTrnWHFzKQHVpYOBJ0tvlghQ2etiEfDN9vySUNbvnc4ZqPvAtSTasz79LojNt5BSCpXgtPICAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e47362dc27e8948ca72620079caeb7fc4086c89e98bf9c7058f365c9bbb1e1ac","last_reissued_at":"2026-05-18T02:16:09.858345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:09.858345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0711.0112","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":"2026-05-18T02:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/Z73GjsKw7B03kN6qOnu2vMEYL8ePGuYujjO+y3ZTORyWVP7QxKVRdbyUI23/XK0MSaakqpJD2p8FqejKRADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:17:20.465981Z"},"content_sha256":"e37bdfb8db0554469e553a4910d69bc529485805b7193a5069056d7a0aa63ea2","schema_version":"1.0","event_id":"sha256:e37bdfb8db0554469e553a4910d69bc529485805b7193a5069056d7a0aa63ea2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:4RZWFXBH5CKIZJZGEADZZLVX7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Photon position eigenvectors lead to complete photon wave mechanics","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Margaret Hawton","submitted_at":"2007-11-01T15:40:37Z","abstract_excerpt":"We have recently constructed a photon position operator with commuting components. This was long thought to be impossible, but our position eigenvectors have a vortex structure like twisted light. Thus they are not spherically symmetric and the position operator does not transform as a vector, so that previous non-existence arguments do not apply. We find two classes of position eigenvectors and obtain photon wave functions by projection onto the bases of position eigenkets that they define, following the usual rules of quantum mechanics. The hermitian position operator, r0, leads to a Landau-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0112","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":"2026-05-18T02:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n864490woUF9eOaf93b3BjrIZ8EBMWgrBluhbjslnQIeyKJJqWixZ5hS2smH9dk8D7KvQtHzBldGhvGKGwprCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:17:20.466346Z"},"content_sha256":"55ae1cb3bd9268b17d334763e1368e23b9ccba150f64a02cb9ac1c7b19cc9b2c","schema_version":"1.0","event_id":"sha256:55ae1cb3bd9268b17d334763e1368e23b9ccba150f64a02cb9ac1c7b19cc9b2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4RZWFXBH5CKIZJZGEADZZLVX7R/bundle.json","state_url":"https://pith.science/pith/4RZWFXBH5CKIZJZGEADZZLVX7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4RZWFXBH5CKIZJZGEADZZLVX7R/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":"2026-06-02T08:17:20Z","links":{"resolver":"https://pith.science/pith/4RZWFXBH5CKIZJZGEADZZLVX7R","bundle":"https://pith.science/pith/4RZWFXBH5CKIZJZGEADZZLVX7R/bundle.json","state":"https://pith.science/pith/4RZWFXBH5CKIZJZGEADZZLVX7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4RZWFXBH5CKIZJZGEADZZLVX7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:4RZWFXBH5CKIZJZGEADZZLVX7R","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":"c1258017548624c5ea464481f3ef886763e23bdc70aef870e855c65e9138e5c3","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-11-01T15:40:37Z","title_canon_sha256":"30d743a9cabf931764b11dc80e821180247d31418acfa52ac344718bfc99268a"},"schema_version":"1.0","source":{"id":"0711.0112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.0112","created_at":"2026-05-18T02:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"0711.0112v1","created_at":"2026-05-18T02:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0112","created_at":"2026-05-18T02:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"4RZWFXBH5CKI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"4RZWFXBH5CKIZJZG","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"4RZWFXBH","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:55ae1cb3bd9268b17d334763e1368e23b9ccba150f64a02cb9ac1c7b19cc9b2c","target":"graph","created_at":"2026-05-18T02:16:09Z","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 have recently constructed a photon position operator with commuting components. This was long thought to be impossible, but our position eigenvectors have a vortex structure like twisted light. Thus they are not spherically symmetric and the position operator does not transform as a vector, so that previous non-existence arguments do not apply. We find two classes of position eigenvectors and obtain photon wave functions by projection onto the bases of position eigenkets that they define, following the usual rules of quantum mechanics. The hermitian position operator, r0, leads to a Landau-","authors_text":"Margaret Hawton","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-11-01T15:40:37Z","title":"Photon position eigenvectors lead to complete photon wave mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0112","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:e37bdfb8db0554469e553a4910d69bc529485805b7193a5069056d7a0aa63ea2","target":"record","created_at":"2026-05-18T02:16:09Z","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":"c1258017548624c5ea464481f3ef886763e23bdc70aef870e855c65e9138e5c3","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-11-01T15:40:37Z","title_canon_sha256":"30d743a9cabf931764b11dc80e821180247d31418acfa52ac344718bfc99268a"},"schema_version":"1.0","source":{"id":"0711.0112","kind":"arxiv","version":1}},"canonical_sha256":"e47362dc27e8948ca72620079caeb7fc4086c89e98bf9c7058f365c9bbb1e1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e47362dc27e8948ca72620079caeb7fc4086c89e98bf9c7058f365c9bbb1e1ac","first_computed_at":"2026-05-18T02:16:09.858345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:09.858345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zGVf++CEtNW8zTrnWHFzKQHVpYOBJ0tvlghQ2etiEfDN9vySUNbvnc4ZqPvAtSTasz79LojNt5BSCpXgtPICAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:09.858854Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.0112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37bdfb8db0554469e553a4910d69bc529485805b7193a5069056d7a0aa63ea2","sha256:55ae1cb3bd9268b17d334763e1368e23b9ccba150f64a02cb9ac1c7b19cc9b2c"],"state_sha256":"7de2c32796387d9a3ca9c5b6166c2886d7681af9dbd5ebaf04e2cd8099cb1e14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIPVkSQBlYbYva6PwzGKlJKyVluFQf2Esn9J0zVMtOFssl+EG9NT3EHrgnepN3G1q6rCBfPW9i5u7I09xLF5Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:17:20.468284Z","bundle_sha256":"07f4781936436c20b207c0198a738e95a32e88bd504d49120f41bf0663261ab9"}}