{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3LTIX3GGW5QWBE5N6D5V35COQT","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":"d7663240f2f196ad0061bd3e0ca411ec70c588cbfe466ec73cda29cc527cee61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2011-03-24T15:26:44Z","title_canon_sha256":"dfdb4f2391cde84a88402776a97c52c6768e3063ccda8b55aaba2cb100d94ac7"},"schema_version":"1.0","source":{"id":"1103.4785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4785","created_at":"2026-05-18T04:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4785v2","created_at":"2026-05-18T04:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4785","created_at":"2026-05-18T04:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"3LTIX3GGW5QW","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3LTIX3GGW5QWBE5N","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3LTIX3GG","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:78b44062ca1cee104f23ab8715d0be89d37c4cf13c7d85be403a9e7f6bf3ef4f","target":"graph","created_at":"2026-05-18T04:25:04Z","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":"The dynamics of a physical system is linked to its phase-space geometry by Noether's theorem, which holds under standard hypotheses including continuity. Does an analogous theorem hold for discrete systems? As a testbed, we take the Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show that---and why---energy not only acts as a generator of the dynamics for this family of systems, but is also conserved when the dynamics is time-invariant.","authors_text":"Silvio Capobianco, Tommaso Toffoli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2011-03-24T15:26:44Z","title":"Can anything from Noether's theorem be salvaged for discrete dynamical systems?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4785","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":"sha256:03063bbfe95a4fda10154d2c0b573c97162d7c5904531eebc96a4a8531439a41","target":"record","created_at":"2026-05-18T04:25:04Z","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":"d7663240f2f196ad0061bd3e0ca411ec70c588cbfe466ec73cda29cc527cee61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2011-03-24T15:26:44Z","title_canon_sha256":"dfdb4f2391cde84a88402776a97c52c6768e3063ccda8b55aaba2cb100d94ac7"},"schema_version":"1.0","source":{"id":"1103.4785","kind":"arxiv","version":2}},"canonical_sha256":"dae68becc6b7616093adf0fb5df44e84fc8d96fd98833e9499d5ec03358afec1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dae68becc6b7616093adf0fb5df44e84fc8d96fd98833e9499d5ec03358afec1","first_computed_at":"2026-05-18T04:25:04.393036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:04.393036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qhDm7WRdLVhTjAeoZi7uDNknVAfAWGNaDsBufUc4FSxbVWCCtaX3yRqNNis+MwhL7AkQJx9EG3/FSKIQ/b3MAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:04.393447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03063bbfe95a4fda10154d2c0b573c97162d7c5904531eebc96a4a8531439a41","sha256:78b44062ca1cee104f23ab8715d0be89d37c4cf13c7d85be403a9e7f6bf3ef4f"],"state_sha256":"e8bf1838d21d7000fd99c042837f1b4ef4719e1d1adb8c3834c41902a7a4d83b"}