{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QMA6K3V6LUJOQUQDMC7YRQKN6I","short_pith_number":"pith:QMA6K3V6","canonical_record":{"source":{"id":"1805.10358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-25T20:40:04Z","cross_cats_sorted":["cond-mat.soft","math.MP"],"title_canon_sha256":"cc44075be9e2e2b501c3e594e4f3b3f55ad1867cb804c35adaf43d126669fb00","abstract_canon_sha256":"f1376f755e70af2891d81599569d8fe449df5742f7d0fef3572ddf8c9bf75bee"},"schema_version":"1.0"},"canonical_sha256":"8301e56ebe5d12e8520360bf88c14df21ed8bb4fa9371a1da8bbcaf6c64d3b57","source":{"kind":"arxiv","id":"1805.10358","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10358","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10358v2","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10358","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"QMA6K3V6LUJO","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QMA6K3V6LUJOQUQD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QMA6K3V6","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QMA6K3V6LUJOQUQDMC7YRQKN6I","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-25T20:40:04Z","cross_cats_sorted":["cond-mat.soft","math.MP"],"title_canon_sha256":"cc44075be9e2e2b501c3e594e4f3b3f55ad1867cb804c35adaf43d126669fb00","abstract_canon_sha256":"f1376f755e70af2891d81599569d8fe449df5742f7d0fef3572ddf8c9bf75bee"},"schema_version":"1.0"},"canonical_sha256":"8301e56ebe5d12e8520360bf88c14df21ed8bb4fa9371a1da8bbcaf6c64d3b57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:45.477677Z","signature_b64":"+IbMgCBavLvBA9VsbLMBPMRU1aQp6vY+uvdtUs7ljSLq6s0EtOew3ae3P9MXUIiO/MJQ9EL4xzTmbsPMyZikBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8301e56ebe5d12e8520360bf88c14df21ed8bb4fa9371a1da8bbcaf6c64d3b57","last_reissued_at":"2026-05-18T00:05:45.476568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:45.476568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10358","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":"2026-05-18T00:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jjF4RlxwyoW/02Pw20/wDgFfan0hqZdBytvYxCzYo6cYAbNNXc1WsYMjlisvssmC6JOWmpBRRa2ePsM64h5DAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:35:00.234440Z"},"content_sha256":"3faee793c6478afd3c854355809b5e48e8a3158948a4c45fc084abbd78dcf881","schema_version":"1.0","event_id":"sha256:3faee793c6478afd3c854355809b5e48e8a3158948a4c45fc084abbd78dcf881"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QMA6K3V6LUJOQUQDMC7YRQKN6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maxwell's Theory of Solid Angle and the Construction of Knotted Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.MP"],"primary_cat":"math-ph","authors_text":"Gareth P. Alexander, Jack Binysh","submitted_at":"2018-05-25T20:40:04Z","abstract_excerpt":"We provide a systematic description of the solid angle function as a means of constructing a knotted field for any curve or link in $\\mathbb{R}^3$. This is a purely geometric construction in which all of the properties of the entire knotted field derive from the geometry of the curve, and from projective and spherical geometry. We emphasise a fundamental homotopy formula as unifying different formulae for computing the solid angle. The solid angle induces a natural framing of the curve, which we show is related to its writhe and use to characterise the local structure in a neighborhood of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10358","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":""},"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":"2026-05-18T00:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rmk1x+rBF9ku+ny9EpBfNyn9N/RXMpcIWCyvXg2uuLT3HOjESt109Urd6itH076wxkRfkwmnHw9h38kBDSHYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:35:00.234802Z"},"content_sha256":"cc8d0977cc89ea8a2a170a46a3e5dd6fc8ac61ec41b4e6c356a764670f3776dc","schema_version":"1.0","event_id":"sha256:cc8d0977cc89ea8a2a170a46a3e5dd6fc8ac61ec41b4e6c356a764670f3776dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I/bundle.json","state_url":"https://pith.science/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I/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":"2026-05-28T02:35:00Z","links":{"resolver":"https://pith.science/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I","bundle":"https://pith.science/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I/bundle.json","state":"https://pith.science/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMA6K3V6LUJOQUQDMC7YRQKN6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QMA6K3V6LUJOQUQDMC7YRQKN6I","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":"f1376f755e70af2891d81599569d8fe449df5742f7d0fef3572ddf8c9bf75bee","cross_cats_sorted":["cond-mat.soft","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-25T20:40:04Z","title_canon_sha256":"cc44075be9e2e2b501c3e594e4f3b3f55ad1867cb804c35adaf43d126669fb00"},"schema_version":"1.0","source":{"id":"1805.10358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10358","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10358v2","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10358","created_at":"2026-05-18T00:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"QMA6K3V6LUJO","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QMA6K3V6LUJOQUQD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QMA6K3V6","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:cc8d0977cc89ea8a2a170a46a3e5dd6fc8ac61ec41b4e6c356a764670f3776dc","target":"graph","created_at":"2026-05-18T00:05:45Z","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 provide a systematic description of the solid angle function as a means of constructing a knotted field for any curve or link in $\\mathbb{R}^3$. This is a purely geometric construction in which all of the properties of the entire knotted field derive from the geometry of the curve, and from projective and spherical geometry. We emphasise a fundamental homotopy formula as unifying different formulae for computing the solid angle. The solid angle induces a natural framing of the curve, which we show is related to its writhe and use to characterise the local structure in a neighborhood of the ","authors_text":"Gareth P. Alexander, Jack Binysh","cross_cats":["cond-mat.soft","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-25T20:40:04Z","title":"Maxwell's Theory of Solid Angle and the Construction of Knotted Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10358","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":"sha256:3faee793c6478afd3c854355809b5e48e8a3158948a4c45fc084abbd78dcf881","target":"record","created_at":"2026-05-18T00:05:45Z","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":"f1376f755e70af2891d81599569d8fe449df5742f7d0fef3572ddf8c9bf75bee","cross_cats_sorted":["cond-mat.soft","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-25T20:40:04Z","title_canon_sha256":"cc44075be9e2e2b501c3e594e4f3b3f55ad1867cb804c35adaf43d126669fb00"},"schema_version":"1.0","source":{"id":"1805.10358","kind":"arxiv","version":2}},"canonical_sha256":"8301e56ebe5d12e8520360bf88c14df21ed8bb4fa9371a1da8bbcaf6c64d3b57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8301e56ebe5d12e8520360bf88c14df21ed8bb4fa9371a1da8bbcaf6c64d3b57","first_computed_at":"2026-05-18T00:05:45.476568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:45.476568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+IbMgCBavLvBA9VsbLMBPMRU1aQp6vY+uvdtUs7ljSLq6s0EtOew3ae3P9MXUIiO/MJQ9EL4xzTmbsPMyZikBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:45.477677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3faee793c6478afd3c854355809b5e48e8a3158948a4c45fc084abbd78dcf881","sha256:cc8d0977cc89ea8a2a170a46a3e5dd6fc8ac61ec41b4e6c356a764670f3776dc"],"state_sha256":"19f29e80eb764671657c35de286b9aca59ce87eafa93d598146a1c4f1a6cc28f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqZBjjG9tWq8XU2BIxcb4yPRxhMybYVufbRfCUajyf3RqbyuEoeNGIJYdTakGkMDKwmJaFYPLR3mTCejPiWIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:35:00.236864Z","bundle_sha256":"7c8d1530abfa5e92152d402d8a9864c127388a0735b9520ac2e65101a372d665"}}