{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HPNPLFY3Q6DEJRC6NGG3YPMO2B","short_pith_number":"pith:HPNPLFY3","canonical_record":{"source":{"id":"2503.08846","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-03-11T19:35:24Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"title_canon_sha256":"e77c37197882346e2dcdc9613ad90847e4bde8c5e24ef726ed0d7620e5280699","abstract_canon_sha256":"ef2d5554f0b82a9bb4c7cc6da6cb6591366b75d509f370686f8575f2a42a5733"},"schema_version":"1.0"},"canonical_sha256":"3bdaf5971b878644c45e698dbc3d8ed0779c59e53f7d1cb2ea45963dd8a0a9bc","source":{"kind":"arxiv","id":"2503.08846","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.08846","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"2503.08846v2","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08846","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"HPNPLFY3Q6DE","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"pith_short_16","alias_value":"HPNPLFY3Q6DEJRC6","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"pith_short_8","alias_value":"HPNPLFY3","created_at":"2026-07-05T11:43:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HPNPLFY3Q6DEJRC6NGG3YPMO2B","target":"record","payload":{"canonical_record":{"source":{"id":"2503.08846","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-03-11T19:35:24Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"title_canon_sha256":"e77c37197882346e2dcdc9613ad90847e4bde8c5e24ef726ed0d7620e5280699","abstract_canon_sha256":"ef2d5554f0b82a9bb4c7cc6da6cb6591366b75d509f370686f8575f2a42a5733"},"schema_version":"1.0"},"canonical_sha256":"3bdaf5971b878644c45e698dbc3d8ed0779c59e53f7d1cb2ea45963dd8a0a9bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:31.085069Z","signature_b64":"SB1gxyk8lgSepYeY/nbsCAyGkZzXPKtY2LFz/vab1Ct+qLQQxYd5U5Gf6+a+qjOa6DrLDX+QQIjlYpW/0lRLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bdaf5971b878644c45e698dbc3d8ed0779c59e53f7d1cb2ea45963dd8a0a9bc","last_reissued_at":"2026-07-05T11:43:31.084568Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:31.084568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.08846","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":"2026-07-05T11:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1LlsuZ49jmnnwdODrnBQC81VsX5O5hkgzSP3cBWql9Y4zW8pumERFp5cthLFG59fEy2GRMnKc6+eb6A8aWBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:24:28.894626Z"},"content_sha256":"1e16f521c2af5f52d7a60b0a996b75fec248afe4402e6527b53d752c6ef1f124","schema_version":"1.0","event_id":"sha256:1e16f521c2af5f52d7a60b0a996b75fec248afe4402e6527b53d752c6ef1f124"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HPNPLFY3Q6DEJRC6NGG3YPMO2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Tutorial on Knots and Quantum Mechanics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th"],"primary_cat":"quant-ph","authors_text":"Dmitry Melnikov","submitted_at":"2025-03-11T19:35:24Z","abstract_excerpt":"These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by the topology of spaces that are used as modules to build the quantum mechanical model, while expectation values and probabilities are given by topological invariants of spaces, knots and links. The notes focus on the specific way the topology encodes quantum mechanical features, or, equivalently, on how these features can be controlled through the topology. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08846","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.08846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VI4RkuOojU3nhnVZLXKYYUTs7Hfc52ElnZBp4c04oM0T6LSmDwbdyOe0874mw4mVu04GxvXRa7KVmHm0sY/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:24:28.895195Z"},"content_sha256":"b3b9ca8524de20e37b1a559c5162aeadea3767363aee241e8aff540e235c82d6","schema_version":"1.0","event_id":"sha256:b3b9ca8524de20e37b1a559c5162aeadea3767363aee241e8aff540e235c82d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B/bundle.json","state_url":"https://pith.science/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B/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":"2026-08-16T01:24:28Z","links":{"resolver":"https://pith.science/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B","bundle":"https://pith.science/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B/bundle.json","state":"https://pith.science/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPNPLFY3Q6DEJRC6NGG3YPMO2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HPNPLFY3Q6DEJRC6NGG3YPMO2B","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":"ef2d5554f0b82a9bb4c7cc6da6cb6591366b75d509f370686f8575f2a42a5733","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-03-11T19:35:24Z","title_canon_sha256":"e77c37197882346e2dcdc9613ad90847e4bde8c5e24ef726ed0d7620e5280699"},"schema_version":"1.0","source":{"id":"2503.08846","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.08846","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"2503.08846v2","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08846","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"HPNPLFY3Q6DE","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"pith_short_16","alias_value":"HPNPLFY3Q6DEJRC6","created_at":"2026-07-05T11:43:31Z"},{"alias_kind":"pith_short_8","alias_value":"HPNPLFY3","created_at":"2026-07-05T11:43:31Z"}],"graph_snapshots":[{"event_id":"sha256:b3b9ca8524de20e37b1a559c5162aeadea3767363aee241e8aff540e235c82d6","target":"graph","created_at":"2026-07-05T11:43:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.08846/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by the topology of spaces that are used as modules to build the quantum mechanical model, while expectation values and probabilities are given by topological invariants of spaces, knots and links. The notes focus on the specific way the topology encodes quantum mechanical features, or, equivalently, on how these features can be controlled through the topology. ","authors_text":"Dmitry Melnikov","cross_cats":["cond-mat.mes-hall","hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-03-11T19:35:24Z","title":"A Tutorial on Knots and Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08846","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":"sha256:1e16f521c2af5f52d7a60b0a996b75fec248afe4402e6527b53d752c6ef1f124","target":"record","created_at":"2026-07-05T11:43:31Z","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":"ef2d5554f0b82a9bb4c7cc6da6cb6591366b75d509f370686f8575f2a42a5733","cross_cats_sorted":["cond-mat.mes-hall","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-03-11T19:35:24Z","title_canon_sha256":"e77c37197882346e2dcdc9613ad90847e4bde8c5e24ef726ed0d7620e5280699"},"schema_version":"1.0","source":{"id":"2503.08846","kind":"arxiv","version":2}},"canonical_sha256":"3bdaf5971b878644c45e698dbc3d8ed0779c59e53f7d1cb2ea45963dd8a0a9bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bdaf5971b878644c45e698dbc3d8ed0779c59e53f7d1cb2ea45963dd8a0a9bc","first_computed_at":"2026-07-05T11:43:31.084568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:31.084568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SB1gxyk8lgSepYeY/nbsCAyGkZzXPKtY2LFz/vab1Ct+qLQQxYd5U5Gf6+a+qjOa6DrLDX+QQIjlYpW/0lRLAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:31.085069Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.08846","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e16f521c2af5f52d7a60b0a996b75fec248afe4402e6527b53d752c6ef1f124","sha256:b3b9ca8524de20e37b1a559c5162aeadea3767363aee241e8aff540e235c82d6"],"state_sha256":"441fcc47eea839147e87bdf936c77fee037b5cbb1bc439a1ee575b3e4801d104"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75KPcEXA4uOSdEtImb3L+OfABjH81SaL5g5Z/WBNcm+GdKhLm3ZlWM6TuIkJ6ANENG30dyzcxG+kj0k6bqEaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T01:24:28.899593Z","bundle_sha256":"b8d2e627a17ad72d054c4fc40cc92e7a3891401f6aa47ef6df851c8019fd6702"}}