{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:H3NZX7A6U2GQJZLJFL2C4BDZWB","short_pith_number":"pith:H3NZX7A6","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"},"canonical_sha256":"3edb9bfc1ea68d04e5692af42e0479b06363f59d343e7cb4fe5223d6e268ab31","source":{"kind":"arxiv","id":"2505.23976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23976","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23976v1","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23976","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"pith_short_12","alias_value":"H3NZX7A6U2GQ","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"pith_short_16","alias_value":"H3NZX7A6U2GQJZLJ","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"pith_short_8","alias_value":"H3NZX7A6","created_at":"2026-07-05T11:12:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:H3NZX7A6U2GQJZLJFL2C4BDZWB","target":"record","payload":{"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"},"canonical_sha256":"3edb9bfc1ea68d04e5692af42e0479b06363f59d343e7cb4fe5223d6e268ab31","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"},"source_kind":"arxiv","source_id":"2505.23976","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:12:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lFoLaK/hCcYRiO0z8GpT8vRWKneEWxz6IGUQfWkXoEVpnU4FbVqBWrRQv8TLMRXVpx4AySxJuYkO0HndpCKICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:50:17.454013Z"},"content_sha256":"4f3bfcd7233c3ec3f3829df98a4a0aefaf4d24c0b6eb1009fa014f81746ef7cd","schema_version":"1.0","event_id":"sha256:4f3bfcd7233c3ec3f3829df98a4a0aefaf4d24c0b6eb1009fa014f81746ef7cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:H3NZX7A6U2GQJZLJFL2C4BDZWB","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:12:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j9tioE8lCuf0mS1OGlV1K5TFy5mfYw1IhLTt1/an3SB/OToMegS2Y861u5A7daTII7GorbHnvEnZamHI0eLZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:50:17.511079Z"},"content_sha256":"e3f0beed38c5c1249e751794aed2a57740277671a9bdab44f8d8ee4cf52f4650","schema_version":"1.0","event_id":"sha256:e3f0beed38c5c1249e751794aed2a57740277671a9bdab44f8d8ee4cf52f4650"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/bundle.json","state_url":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T22:50:17Z","links":{"resolver":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB","bundle":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/bundle.json","state":"https://pith.science/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3NZX7A6U2GQJZLJFL2C4BDZWB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:H3NZX7A6U2GQJZLJFL2C4BDZWB","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":"003964cb9f9ce09d3b75e378fd280c550dd434240ba80b88849bfadd0fe300fd","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-29T20:00:47Z","title_canon_sha256":"20a1b801e0d23293cf7a37384bc4a0fa2da73ca6703ecff624aad3b1387fcd18"},"schema_version":"1.0","source":{"id":"2505.23976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23976","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23976v1","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23976","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"pith_short_12","alias_value":"H3NZX7A6U2GQ","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"pith_short_16","alias_value":"H3NZX7A6U2GQJZLJ","created_at":"2026-07-05T11:12:39Z"},{"alias_kind":"pith_short_8","alias_value":"H3NZX7A6","created_at":"2026-07-05T11:12:39Z"}],"graph_snapshots":[{"event_id":"sha256:e3f0beed38c5c1249e751794aed2a57740277671a9bdab44f8d8ee4cf52f4650","target":"graph","created_at":"2026-07-05T11:12:39Z","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/2505.23976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Davi Lopes Medeiros, Emanoel Souza, Euripedes Carvalho da Silva","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-29T20:00:47Z","title":"On the minimality of pancake decomposition of surface germs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23976","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":"sha256:4f3bfcd7233c3ec3f3829df98a4a0aefaf4d24c0b6eb1009fa014f81746ef7cd","target":"record","created_at":"2026-07-05T11:12:39Z","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":"003964cb9f9ce09d3b75e378fd280c550dd434240ba80b88849bfadd0fe300fd","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-29T20:00:47Z","title_canon_sha256":"20a1b801e0d23293cf7a37384bc4a0fa2da73ca6703ecff624aad3b1387fcd18"},"schema_version":"1.0","source":{"id":"2505.23976","kind":"arxiv","version":1}},"canonical_sha256":"3edb9bfc1ea68d04e5692af42e0479b06363f59d343e7cb4fe5223d6e268ab31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3edb9bfc1ea68d04e5692af42e0479b06363f59d343e7cb4fe5223d6e268ab31","first_computed_at":"2026-07-05T11:12:39.356506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:39.356506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qNkGvLMlSOUFHBCx3jeB4xb2RlpYwNr6lpv46o+4AM/SciU8eolqfx0t0m19sE90fwtDVAfFfWkcuzL+NrE0AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:39.357017Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.23976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f3bfcd7233c3ec3f3829df98a4a0aefaf4d24c0b6eb1009fa014f81746ef7cd","sha256:e3f0beed38c5c1249e751794aed2a57740277671a9bdab44f8d8ee4cf52f4650"],"state_sha256":"b75dc8c68110f925aa4ca3384e60340b0278aff8e92623c5e06fba0ce317a45b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7ck5OXTq2jJ8pATJtETxr1cod4KGsdbnN7u8FSbMcAh16kSm+yFNsIEq9IxyePWwHKT2gwQckwVwidRq/puAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T22:50:17.519093Z","bundle_sha256":"cdafcffb2cf5d39f26333c69ef8a7e92faedd66785fc86aaa61d74c45d985363"}}