{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:IZIMH4WL54SAWSAUIEGNBW4PJH","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":"5bd23c8e38d0c5e0ba38c760e0965b98a861b8062c894a206355ccd2981a942c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-04T18:39:03Z","title_canon_sha256":"06bd01d799ec4418c768d8156ba6bbf90b7a74dac00e1056609fbccab0064d40"},"schema_version":"1.0","source":{"id":"2412.03543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.03543","created_at":"2026-07-05T09:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"2412.03543v1","created_at":"2026-07-05T09:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.03543","created_at":"2026-07-05T09:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"IZIMH4WL54SA","created_at":"2026-07-05T09:44:30Z"},{"alias_kind":"pith_short_16","alias_value":"IZIMH4WL54SAWSAU","created_at":"2026-07-05T09:44:30Z"},{"alias_kind":"pith_short_8","alias_value":"IZIMH4WL","created_at":"2026-07-05T09:44:30Z"}],"graph_snapshots":[{"event_id":"sha256:4f3524fbcfa712c4d1f8851e96bcb439130f5bb8bfe4815312ac41a28510582e","target":"graph","created_at":"2026-07-05T09:44:30Z","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/2412.03543/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these generic equations. Furthermore, we show that these equations can be reinterpreted as difference systems defined on the ${\\mathbb Z}^2$ graph and this reinterpretation relates (unifies) the linear and the non-linear approach of discrete analytic functions.","authors_text":"Maciej Nieszporski, Pavlos Kassotakis, Theodoros Kouloukas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-04T18:39:03Z","title":"Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03543","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:ed6600b13cd39cab9566da8fd8934099275fb67e1a181ce25335277e5649052f","target":"record","created_at":"2026-07-05T09:44:30Z","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":"5bd23c8e38d0c5e0ba38c760e0965b98a861b8062c894a206355ccd2981a942c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2024-12-04T18:39:03Z","title_canon_sha256":"06bd01d799ec4418c768d8156ba6bbf90b7a74dac00e1056609fbccab0064d40"},"schema_version":"1.0","source":{"id":"2412.03543","kind":"arxiv","version":1}},"canonical_sha256":"4650c3f2cbef240b4814410cd0db8f49d20a57862a783cdeb4603a0f72da2fd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4650c3f2cbef240b4814410cd0db8f49d20a57862a783cdeb4603a0f72da2fd7","first_computed_at":"2026-07-05T09:44:30.990483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:44:30.990483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zoCB1USkExL9jauGqfGNyqtRwg+YOGy2pE0Ipi8YJP5jVAgglQYPyrMWMuHxT6epuUrIIUgMs/U4ctLs4LLwBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:44:30.990987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.03543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed6600b13cd39cab9566da8fd8934099275fb67e1a181ce25335277e5649052f","sha256:4f3524fbcfa712c4d1f8851e96bcb439130f5bb8bfe4815312ac41a28510582e"],"state_sha256":"18bc29f0a2814f164cb81bfe86b13cf9734782202fac0554af057e441bf76fb9"}