{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OAC6WFNORDDOMDRIEHAAOYFCTL","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":"ed37e7289bf06365b0733df742220b6f8cf8b68618426b3432c259f44d12fa8d","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-04T16:14:14Z","title_canon_sha256":"ccc1d4525eed5120b21a712e1b3ef47f21904185a0687e782297faf550631a68"},"schema_version":"1.0","source":{"id":"1312.1229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1229","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1229v1","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1229","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"OAC6WFNORDDO","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OAC6WFNORDDOMDRI","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OAC6WFNO","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d2db7b891c0218e6815531720deca5bc9ea9c6b5841733780b697649cd6d0825","target":"graph","created_at":"2026-05-18T03:05:34Z","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":"Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to differential equations in the time variable. If these real dynamical variables are instead replaced by integers, and also the time variable is restricted to integers, it appears to be hard to enforce energy conservation unless one can also derive a Hamiltonian formalism for that case. We here show how the Hamiltonian formalism works here, and how it may yield the us","authors_text":"Gerard 't Hooft","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-04T16:14:14Z","title":"Hamiltonian formalism for integer-valued variables and integer time steps and a possible application in quantum physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1229","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":"sha256:43789b1dbab3befa67584811adfdffb31b3ce53c1793e5828d75f2f994ad3c87","target":"record","created_at":"2026-05-18T03:05:34Z","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":"ed37e7289bf06365b0733df742220b6f8cf8b68618426b3432c259f44d12fa8d","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-04T16:14:14Z","title_canon_sha256":"ccc1d4525eed5120b21a712e1b3ef47f21904185a0687e782297faf550631a68"},"schema_version":"1.0","source":{"id":"1312.1229","kind":"arxiv","version":1}},"canonical_sha256":"7005eb15ae88c6e60e2821c00760a29acaf238f2496deac4e805ad4963deac0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7005eb15ae88c6e60e2821c00760a29acaf238f2496deac4e805ad4963deac0d","first_computed_at":"2026-05-18T03:05:34.596668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:34.596668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f44qt3/DwiVwZCtztG+tFskApuod0scoRo/K+sLgQN69z2nDW9wwll4CDDr8kxbn+EQ+5Ss1I0Z1SRbGpsUeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:34.597102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43789b1dbab3befa67584811adfdffb31b3ce53c1793e5828d75f2f994ad3c87","sha256:d2db7b891c0218e6815531720deca5bc9ea9c6b5841733780b697649cd6d0825"],"state_sha256":"5f5fc2aff5fa231bb1c48609b68112c9b694d8ef893c52c078f6d934a47f94d6"}