{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UL5MYKS6FKJGPXNRCYBDDKFA6V","short_pith_number":"pith:UL5MYKS6","schema_version":"1.0","canonical_sha256":"a2facc2a5e2a9267ddb1160231a8a0f55c6b6fe0589c7081e242245c7e4ca146","source":{"kind":"arxiv","id":"1611.06257","version":3},"attestation_state":"computed","paper":{"title":"Field Patterns: A New Mathematical Object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.optics","authors_text":"Graeme W. Milton, Ornella Mattei","submitted_at":"2016-11-18T21:40:23Z","abstract_excerpt":"Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patt"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.06257","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2016-11-18T21:40:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b2b55e18f9eb953c86718d839e32effe7bc303c71757427c0048bb4ff5560dd2","abstract_canon_sha256":"cfdd5f76d6e9f226a84f3b95d4e082490e4ccdf7659fe08e42431083decf2a70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:51.879024Z","signature_b64":"8YimUsuctLuXiOIN6Hg9wI7i8Ui6r0Po0a36WGSpiapLXY2dtEATaIgYGI6q7EqAmri+oHaYyhnjzAZBMN+RAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2facc2a5e2a9267ddb1160231a8a0f55c6b6fe0589c7081e242245c7e4ca146","last_reissued_at":"2026-05-18T00:50:51.878495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:51.878495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Field Patterns: A New Mathematical Object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.optics","authors_text":"Graeme W. Milton, Ornella Mattei","submitted_at":"2016-11-18T21:40:23Z","abstract_excerpt":"Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06257","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.06257","created_at":"2026-05-18T00:50:51.878554+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06257v3","created_at":"2026-05-18T00:50:51.878554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06257","created_at":"2026-05-18T00:50:51.878554+00:00"},{"alias_kind":"pith_short_12","alias_value":"UL5MYKS6FKJG","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UL5MYKS6FKJGPXNR","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UL5MYKS6","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V","json":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V.json","graph_json":"https://pith.science/api/pith-number/UL5MYKS6FKJGPXNRCYBDDKFA6V/graph.json","events_json":"https://pith.science/api/pith-number/UL5MYKS6FKJGPXNRCYBDDKFA6V/events.json","paper":"https://pith.science/paper/UL5MYKS6"},"agent_actions":{"view_html":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V","download_json":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V.json","view_paper":"https://pith.science/paper/UL5MYKS6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06257&json=true","fetch_graph":"https://pith.science/api/pith-number/UL5MYKS6FKJGPXNRCYBDDKFA6V/graph.json","fetch_events":"https://pith.science/api/pith-number/UL5MYKS6FKJGPXNRCYBDDKFA6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V/action/storage_attestation","attest_author":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V/action/author_attestation","sign_citation":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V/action/citation_signature","submit_replication":"https://pith.science/pith/UL5MYKS6FKJGPXNRCYBDDKFA6V/action/replication_record"}},"created_at":"2026-05-18T00:50:51.878554+00:00","updated_at":"2026-05-18T00:50:51.878554+00:00"}