{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T2KQYKDRLK32DZOZLQB7RH74OC","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":"64c50594a1c6bf620cd8285acf5ccdcbbcac51580d044f4360e699933a6cfb21","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-03T13:35:28Z","title_canon_sha256":"32c6f9f4ea227fa0bfd7f8ae29bb614f9ddd75249332d4a0cc3d901e1545b634"},"schema_version":"1.0","source":{"id":"1602.01294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01294","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01294v1","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01294","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"T2KQYKDRLK32","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T2KQYKDRLK32DZOZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T2KQYKDR","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:c2789578429bd83c7fdb34c8e33f5671eb9a15163b921b098eefcf633c47456e","target":"graph","created_at":"2026-05-18T00:23:59Z","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 consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential $V$ and is subjected to a restoring force of potential $U$. We assume that $U$ and $V$ are even nonnegative polynomials of degree $2\\sigma_1$ and $2\\sigma_2$. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a perturbation. This is an extension to the case $\\sigma_1 < 2\\sigma_2-1$ of some already known results obtained for","authors_text":"Carlo Marchioro, Paolo Butt\\`a","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-03T13:35:28Z","title":"Dynamics of infinite classical anharmonic crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01294","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":"sha256:0ae2197b84a6e1a5b1330722fa22d6e8704111a5598396d47bbf9dfd2427db2d","target":"record","created_at":"2026-05-18T00:23:59Z","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":"64c50594a1c6bf620cd8285acf5ccdcbbcac51580d044f4360e699933a6cfb21","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-03T13:35:28Z","title_canon_sha256":"32c6f9f4ea227fa0bfd7f8ae29bb614f9ddd75249332d4a0cc3d901e1545b634"},"schema_version":"1.0","source":{"id":"1602.01294","kind":"arxiv","version":1}},"canonical_sha256":"9e950c28715ab7a1e5d95c03f89ffc70b8a8558db8f95c7f6f1be01e98f26b89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e950c28715ab7a1e5d95c03f89ffc70b8a8558db8f95c7f6f1be01e98f26b89","first_computed_at":"2026-05-18T00:23:59.287615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:59.287615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kCeHugYId2y8GgHOs8PN3vLsFk11LGBVfAGgYhQTAIG1aPUQ+Qa+UfNrMx38TQKCtT0rwMQbzPZLfPXYo2jJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:59.288326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ae2197b84a6e1a5b1330722fa22d6e8704111a5598396d47bbf9dfd2427db2d","sha256:c2789578429bd83c7fdb34c8e33f5671eb9a15163b921b098eefcf633c47456e"],"state_sha256":"d3d4af39e4e4e0d6633195090c811522452708a46538f3827ab293dd2386f5d2"}