{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:H3NZX7A6U2GQJZLJFL2C4BDZWB","short_pith_number":"pith:H3NZX7A6","schema_version":"1.0","canonical_sha256":"3edb9bfc1ea68d04e5692af42e0479b06363f59d343e7cb4fe5223d6e268ab31","source":{"kind":"arxiv","id":"2505.23976","version":1},"attestation_state":"computed","paper":{"title":"On the minimality of pancake decomposition of surface germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.MG","authors_text":"Davi Lopes Medeiros, Emanoel Souza, Euripedes Carvalho da Silva","submitted_at":"2025-05-29T20:00:47Z","abstract_excerpt":"The abnormal surfaces called snakes and circular snakes, defined in \\cite{GabrielovSouza}, are special types of surface germs capturing the outer Lipschitz phenomena relevant to the outer classification problem. We provide algorithms to obtain a minimal pancake decomposition, i.e., where the number of pancakes is minimal, for snakes and circular snakes. We call a pancake decomposition obtained from our algorithm a greedy pancake decomposition. We also prove that greedy pancake decompositions of weakly outer Lipschitz equivalent snakes (or circular snakes) are weakly equivalent, in the sense th"},"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":"2505.23976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-29T20:00:47Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"20a1b801e0d23293cf7a37384bc4a0fa2da73ca6703ecff624aad3b1387fcd18","abstract_canon_sha256":"003964cb9f9ce09d3b75e378fd280c550dd434240ba80b88849bfadd0fe300fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:39.357017Z","signature_b64":"qNkGvLMlSOUFHBCx3jeB4xb2RlpYwNr6lpv46o+4AM/SciU8eolqfx0t0m19sE90fwtDVAfFfWkcuzL+NrE0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3edb9bfc1ea68d04e5692af42e0479b06363f59d343e7cb4fe5223d6e268ab31","last_reissued_at":"2026-07-05T11:12:39.356506Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:39.356506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the minimality of pancake decomposition of surface germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.MG","authors_text":"Davi Lopes Medeiros, Emanoel Souza, Euripedes Carvalho da Silva","submitted_at":"2025-05-29T20:00:47Z","abstract_excerpt":"The abnormal surfaces called snakes and circular snakes, defined in \\cite{GabrielovSouza}, are special types of surface germs capturing the outer Lipschitz phenomena relevant to the outer classification problem. We provide algorithms to obtain a minimal pancake decomposition, i.e., where the number of pancakes is minimal, for snakes and circular snakes. We call a pancake decomposition obtained from our algorithm a greedy pancake decomposition. We also prove that greedy pancake decompositions of weakly outer Lipschitz equivalent snakes (or circular snakes) are weakly equivalent, in the sense th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23976","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.23976/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.23976","created_at":"2026-07-05T11:12:39.356573+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.23976v1","created_at":"2026-07-05T11:12:39.356573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23976","created_at":"2026-07-05T11:12:39.356573+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3NZX7A6U2GQ","created_at":"2026-07-05T11:12:39.356573+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3NZX7A6U2GQJZLJ","created_at":"2026-07-05T11:12:39.356573+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3NZX7A6","created_at":"2026-07-05T11:12:39.356573+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/H3NZX7A6U2GQJZLJFL2C4BDZWB","json":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB.json","graph_json":"https://pith.science/api/pith-number/H3NZX7A6U2GQJZLJFL2C4BDZWB/graph.json","events_json":"https://pith.science/api/pith-number/H3NZX7A6U2GQJZLJFL2C4BDZWB/events.json","paper":"https://pith.science/paper/H3NZX7A6"},"agent_actions":{"view_html":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB","download_json":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB.json","view_paper":"https://pith.science/paper/H3NZX7A6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.23976&json=true","fetch_graph":"https://pith.science/api/pith-number/H3NZX7A6U2GQJZLJFL2C4BDZWB/graph.json","fetch_events":"https://pith.science/api/pith-number/H3NZX7A6U2GQJZLJFL2C4BDZWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/action/storage_attestation","attest_author":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/action/author_attestation","sign_citation":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/action/citation_signature","submit_replication":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/action/replication_record"}},"created_at":"2026-07-05T11:12:39.356573+00:00","updated_at":"2026-07-05T11:12:39.356573+00:00"}