{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VJVKILCF5MQ27WJR67XPKAHR6C","short_pith_number":"pith:VJVKILCF","schema_version":"1.0","canonical_sha256":"aa6aa42c45eb21afd931f7eef500f1f08a3862e07286262373f0a346c4f3f6a3","source":{"kind":"arxiv","id":"1508.05885","version":1},"attestation_state":"computed","paper":{"title":"Continuous self-similarity in parametric piecewise isometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Franco Vivaldi, John H Lowenstein","submitted_at":"2015-08-24T17:33:05Z","abstract_excerpt":"We exhibit two distinct renormalization scenarios in many-parameter families of piecewise isometries (PWI) of a rhombus. The rotational component, defined over the quadratic field $\\mathbb{K}=\\mathbb{Q}(\\sqrt{5})$, is fixed. The translations are specified by affine functions of the parameters, with coefficients in $\\mathbb{K}$. In each case the parameters range over a convex domain. In one scenario the PWI is self-similar if and only if one parameter belongs to $\\mathbb{K}$, while the other is free. Such a continuous self-similarity is due to the possibility of merging adjacent atoms of an ind"},"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":"1508.05885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-24T17:33:05Z","cross_cats_sorted":[],"title_canon_sha256":"f19ee9624bb92c9295e1c0cd64285be28fd134abdfbf0adadd80273e14719b96","abstract_canon_sha256":"c4f98154072a8649713730b155acfc33afce6207271944b71c1d83974e69c862"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:51.489586Z","signature_b64":"KXqNRZjsVBEaBpIaGjlEUCoKMzEJI/i2j+6SshyLsVSfxR6RwB44wnqR7kQAUz1wo4f+rhjp0C+zy/gpQ9U0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa6aa42c45eb21afd931f7eef500f1f08a3862e07286262373f0a346c4f3f6a3","last_reissued_at":"2026-05-18T01:34:51.488952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:51.488952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuous self-similarity in parametric piecewise isometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Franco Vivaldi, John H Lowenstein","submitted_at":"2015-08-24T17:33:05Z","abstract_excerpt":"We exhibit two distinct renormalization scenarios in many-parameter families of piecewise isometries (PWI) of a rhombus. The rotational component, defined over the quadratic field $\\mathbb{K}=\\mathbb{Q}(\\sqrt{5})$, is fixed. The translations are specified by affine functions of the parameters, with coefficients in $\\mathbb{K}$. In each case the parameters range over a convex domain. In one scenario the PWI is self-similar if and only if one parameter belongs to $\\mathbb{K}$, while the other is free. Such a continuous self-similarity is due to the possibility of merging adjacent atoms of an ind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05885","kind":"arxiv","version":1},"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":"1508.05885","created_at":"2026-05-18T01:34:51.489041+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.05885v1","created_at":"2026-05-18T01:34:51.489041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05885","created_at":"2026-05-18T01:34:51.489041+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJVKILCF5MQ2","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJVKILCF5MQ27WJR","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJVKILCF","created_at":"2026-05-18T12:29:44.643036+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/VJVKILCF5MQ27WJR67XPKAHR6C","json":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C.json","graph_json":"https://pith.science/api/pith-number/VJVKILCF5MQ27WJR67XPKAHR6C/graph.json","events_json":"https://pith.science/api/pith-number/VJVKILCF5MQ27WJR67XPKAHR6C/events.json","paper":"https://pith.science/paper/VJVKILCF"},"agent_actions":{"view_html":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C","download_json":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C.json","view_paper":"https://pith.science/paper/VJVKILCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.05885&json=true","fetch_graph":"https://pith.science/api/pith-number/VJVKILCF5MQ27WJR67XPKAHR6C/graph.json","fetch_events":"https://pith.science/api/pith-number/VJVKILCF5MQ27WJR67XPKAHR6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C/action/storage_attestation","attest_author":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C/action/author_attestation","sign_citation":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C/action/citation_signature","submit_replication":"https://pith.science/pith/VJVKILCF5MQ27WJR67XPKAHR6C/action/replication_record"}},"created_at":"2026-05-18T01:34:51.489041+00:00","updated_at":"2026-05-18T01:34:51.489041+00:00"}