{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CKGQWOI5B5GHS7WS2FAJM4C2EB","short_pith_number":"pith:CKGQWOI5","canonical_record":{"source":{"id":"1503.00713","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-03-02T23:31:37Z","cross_cats_sorted":["cs.IT","gr-qc","math.IT","quant-ph"],"title_canon_sha256":"891c6651dec8da2ea4d8c8f7f093e6baef323452a1018ab9f2f3c45d317fbeaf","abstract_canon_sha256":"45414a3c6da34996f889ac88e23a01a4fce0fb4d80a41978c1ab748d7d7eeaea"},"schema_version":"1.0"},"canonical_sha256":"128d0b391d0f4c797ed2d14096705a2045513d56e85d99a4a7b6f12fc4f98078","source":{"kind":"arxiv","id":"1503.00713","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00713","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00713v4","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00713","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"CKGQWOI5B5GH","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CKGQWOI5B5GHS7WS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CKGQWOI5","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CKGQWOI5B5GHS7WS2FAJM4C2EB","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00713","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-03-02T23:31:37Z","cross_cats_sorted":["cs.IT","gr-qc","math.IT","quant-ph"],"title_canon_sha256":"891c6651dec8da2ea4d8c8f7f093e6baef323452a1018ab9f2f3c45d317fbeaf","abstract_canon_sha256":"45414a3c6da34996f889ac88e23a01a4fce0fb4d80a41978c1ab748d7d7eeaea"},"schema_version":"1.0"},"canonical_sha256":"128d0b391d0f4c797ed2d14096705a2045513d56e85d99a4a7b6f12fc4f98078","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:03.337310Z","signature_b64":"UKG3P1vdqOi69xXKnU0BtRBqbK5cE2yK4ts4YBkgzwSdSGfzWxhQLVXHhcrn3jg0Rj00JGkHVlF/NBU/ihEABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"128d0b391d0f4c797ed2d14096705a2045513d56e85d99a4a7b6f12fc4f98078","last_reissued_at":"2026-05-18T00:43:03.336626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:03.336626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00713","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZtXJOg8JLrqOx/RfoBIz/YoHIsJt0dMw0el7CcUSzHfJ8d3nfANQ1ce20QBZ8FGJsl+KFfVvbHTLbKcwJLmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T05:34:46.722816Z"},"content_sha256":"1d87d3bf022a01c1fdd34f25b1f32cef6469e9df363c33b2e929b717e90e0871","schema_version":"1.0","event_id":"sha256:1d87d3bf022a01c1fdd34f25b1f32cef6469e9df363c33b2e929b717e90e0871"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CKGQWOI5B5GHS7WS2FAJM4C2EB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The ideal energy of classical lattice dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","gr-qc","math.IT","quant-ph"],"primary_cat":"nlin.CG","authors_text":"Norman Margolus","submitted_at":"2015-03-02T23:31:37Z","abstract_excerpt":"We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00713","kind":"arxiv","version":4},"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":"2026-05-18T00:43:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RrapQnh1t98iFcX5rsSxT0QapyAnKN2VEV1ekIoqfjSQ1Ss3yiPJ7IEE0AEJIgyjwIb75XWkIXgjlBiBD2TtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T05:34:46.723178Z"},"content_sha256":"fa45fa489ed606aaf5158ed00345467e548a00dcc7c15aae7bd6afd157bb77a7","schema_version":"1.0","event_id":"sha256:fa45fa489ed606aaf5158ed00345467e548a00dcc7c15aae7bd6afd157bb77a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB/bundle.json","state_url":"https://pith.science/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB/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":"2026-06-30T05:34:46Z","links":{"resolver":"https://pith.science/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB","bundle":"https://pith.science/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB/bundle.json","state":"https://pith.science/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKGQWOI5B5GHS7WS2FAJM4C2EB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CKGQWOI5B5GHS7WS2FAJM4C2EB","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":"45414a3c6da34996f889ac88e23a01a4fce0fb4d80a41978c1ab748d7d7eeaea","cross_cats_sorted":["cs.IT","gr-qc","math.IT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-03-02T23:31:37Z","title_canon_sha256":"891c6651dec8da2ea4d8c8f7f093e6baef323452a1018ab9f2f3c45d317fbeaf"},"schema_version":"1.0","source":{"id":"1503.00713","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00713","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00713v4","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00713","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"CKGQWOI5B5GH","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CKGQWOI5B5GHS7WS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CKGQWOI5","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:fa45fa489ed606aaf5158ed00345467e548a00dcc7c15aae7bd6afd157bb77a7","target":"graph","created_at":"2026-05-18T00:43:03Z","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 define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.","authors_text":"Norman Margolus","cross_cats":["cs.IT","gr-qc","math.IT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-03-02T23:31:37Z","title":"The ideal energy of classical lattice dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00713","kind":"arxiv","version":4},"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":"sha256:1d87d3bf022a01c1fdd34f25b1f32cef6469e9df363c33b2e929b717e90e0871","target":"record","created_at":"2026-05-18T00:43:03Z","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":"45414a3c6da34996f889ac88e23a01a4fce0fb4d80a41978c1ab748d7d7eeaea","cross_cats_sorted":["cs.IT","gr-qc","math.IT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2015-03-02T23:31:37Z","title_canon_sha256":"891c6651dec8da2ea4d8c8f7f093e6baef323452a1018ab9f2f3c45d317fbeaf"},"schema_version":"1.0","source":{"id":"1503.00713","kind":"arxiv","version":4}},"canonical_sha256":"128d0b391d0f4c797ed2d14096705a2045513d56e85d99a4a7b6f12fc4f98078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"128d0b391d0f4c797ed2d14096705a2045513d56e85d99a4a7b6f12fc4f98078","first_computed_at":"2026-05-18T00:43:03.336626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:03.336626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UKG3P1vdqOi69xXKnU0BtRBqbK5cE2yK4ts4YBkgzwSdSGfzWxhQLVXHhcrn3jg0Rj00JGkHVlF/NBU/ihEABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:03.337310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00713","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d87d3bf022a01c1fdd34f25b1f32cef6469e9df363c33b2e929b717e90e0871","sha256:fa45fa489ed606aaf5158ed00345467e548a00dcc7c15aae7bd6afd157bb77a7"],"state_sha256":"3093b411f6ca8e391af69c952c81ce119d88fb48a585bc6b010898d8cd6c4a56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44uKRs1uQpvUADWhZNav+b8TB4rCTqGon3ygzehEi79uJvuGdqVpGgFjJLUJVev1QwrgWik/Q089wyEcJU6NCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T05:34:46.725652Z","bundle_sha256":"096837abc4b73da13667cbf75b8462c27d1e059836a7382440d54d5ec58389f7"}}