{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SEK2YPCV5ELUL3CW4ENUXYIOLM","short_pith_number":"pith:SEK2YPCV","canonical_record":{"source":{"id":"2505.19814","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-05-26T10:51:47Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bd6bcb6142909dbec6880595c11b7242ed6fa2d23bb92fc33b30bb508717c262","abstract_canon_sha256":"b7ed6e591d083423364a2af0e4d8fb4f6734cb04f3171657174bc8a4c6e0bc08"},"schema_version":"1.0"},"canonical_sha256":"9115ac3c55e91745ec56e11b4be10e5b066e09cd40cd694fe20df5cfa011152c","source":{"kind":"arxiv","id":"2505.19814","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19814","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19814v4","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19814","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"pith_short_12","alias_value":"SEK2YPCV5ELU","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"pith_short_16","alias_value":"SEK2YPCV5ELUL3CW","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"pith_short_8","alias_value":"SEK2YPCV","created_at":"2026-05-26T02:03:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SEK2YPCV5ELUL3CW4ENUXYIOLM","target":"record","payload":{"canonical_record":{"source":{"id":"2505.19814","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-05-26T10:51:47Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bd6bcb6142909dbec6880595c11b7242ed6fa2d23bb92fc33b30bb508717c262","abstract_canon_sha256":"b7ed6e591d083423364a2af0e4d8fb4f6734cb04f3171657174bc8a4c6e0bc08"},"schema_version":"1.0"},"canonical_sha256":"9115ac3c55e91745ec56e11b4be10e5b066e09cd40cd694fe20df5cfa011152c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:03:51.066661Z","signature_b64":"sc/jXyBj37fHno5tlysXEzNCWwG/e+2aIEX8ZZlChbhjMij+e3Uoa75O3vM9bB1IgJxmhC6QzKxLBFmP3yprCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9115ac3c55e91745ec56e11b4be10e5b066e09cd40cd694fe20df5cfa011152c","last_reissued_at":"2026-05-26T02:03:51.065586Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:03:51.065586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.19814","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:03:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BPckxn3dn42ZuwAefYgk0fwbDiNncPvOynBIjgkxZWsu75854brxY6E4IgFaylwIhSS8u2U5H7PpeligZfQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:16:44.963293Z"},"content_sha256":"dd84357bf0498ba27187a4134dda56960e8a05802b41f499f9bae7651ce9c698","schema_version":"1.0","event_id":"sha256:dd84357bf0498ba27187a4134dda56960e8a05802b41f499f9bae7651ce9c698"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SEK2YPCV5ELUL3CW4ENUXYIOLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.LO","authors_text":"Krzysztof Jan Nowak","submitted_at":"2025-05-26T10:51:47Z","abstract_excerpt":"The paper concerns uniform Yomdin-Gromov parametrizations together with an estimate of their number, which generalizes a theorem by Cluckers-Forey-Loeser to arbitrary equicharacteristic zero valued fields with analytic structure. To this end, we establish a certain strong analytic stratification of definable sets, based on a definable non-Archimedean version of Bierstone-Milman's canonical desingularization algorithm from our earlier paper. Other basic tools are: elimination of valued field quantifiers, term description of functions definable in analytic structures, and Lipschitz cell decompos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19814","kind":"arxiv","version":4},"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/2505.19814/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":"2026-05-26T02:03:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vwgvh+4rz9QRhJ3f7yGVmNgSmzWNR+fx6hAIYQWP1aRwlQCiSn0X2xPzYHVw7xTYegMaAMV/n9NO6hVfafN1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:16:44.965309Z"},"content_sha256":"80800fe0baeb37c5b79529921b99f3df443845817a86de595106cecb4f22b65b","schema_version":"1.0","event_id":"sha256:80800fe0baeb37c5b79529921b99f3df443845817a86de595106cecb4f22b65b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM/bundle.json","state_url":"https://pith.science/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM/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":"2026-08-18T02:16:44Z","links":{"resolver":"https://pith.science/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM","bundle":"https://pith.science/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM/bundle.json","state":"https://pith.science/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEK2YPCV5ELUL3CW4ENUXYIOLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SEK2YPCV5ELUL3CW4ENUXYIOLM","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":"b7ed6e591d083423364a2af0e4d8fb4f6734cb04f3171657174bc8a4c6e0bc08","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-05-26T10:51:47Z","title_canon_sha256":"bd6bcb6142909dbec6880595c11b7242ed6fa2d23bb92fc33b30bb508717c262"},"schema_version":"1.0","source":{"id":"2505.19814","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19814","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19814v4","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19814","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"pith_short_12","alias_value":"SEK2YPCV5ELU","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"pith_short_16","alias_value":"SEK2YPCV5ELUL3CW","created_at":"2026-05-26T02:03:51Z"},{"alias_kind":"pith_short_8","alias_value":"SEK2YPCV","created_at":"2026-05-26T02:03:51Z"}],"graph_snapshots":[{"event_id":"sha256:80800fe0baeb37c5b79529921b99f3df443845817a86de595106cecb4f22b65b","target":"graph","created_at":"2026-05-26T02:03:51Z","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/2505.19814/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The paper concerns uniform Yomdin-Gromov parametrizations together with an estimate of their number, which generalizes a theorem by Cluckers-Forey-Loeser to arbitrary equicharacteristic zero valued fields with analytic structure. To this end, we establish a certain strong analytic stratification of definable sets, based on a definable non-Archimedean version of Bierstone-Milman's canonical desingularization algorithm from our earlier paper. Other basic tools are: elimination of valued field quantifiers, term description of functions definable in analytic structures, and Lipschitz cell decompos","authors_text":"Krzysztof Jan Nowak","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-05-26T10:51:47Z","title":"Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19814","kind":"arxiv","version":4},"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:dd84357bf0498ba27187a4134dda56960e8a05802b41f499f9bae7651ce9c698","target":"record","created_at":"2026-05-26T02:03:51Z","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":"b7ed6e591d083423364a2af0e4d8fb4f6734cb04f3171657174bc8a4c6e0bc08","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-05-26T10:51:47Z","title_canon_sha256":"bd6bcb6142909dbec6880595c11b7242ed6fa2d23bb92fc33b30bb508717c262"},"schema_version":"1.0","source":{"id":"2505.19814","kind":"arxiv","version":4}},"canonical_sha256":"9115ac3c55e91745ec56e11b4be10e5b066e09cd40cd694fe20df5cfa011152c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9115ac3c55e91745ec56e11b4be10e5b066e09cd40cd694fe20df5cfa011152c","first_computed_at":"2026-05-26T02:03:51.065586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:03:51.065586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sc/jXyBj37fHno5tlysXEzNCWwG/e+2aIEX8ZZlChbhjMij+e3Uoa75O3vM9bB1IgJxmhC6QzKxLBFmP3yprCQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:03:51.066661Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.19814","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd84357bf0498ba27187a4134dda56960e8a05802b41f499f9bae7651ce9c698","sha256:80800fe0baeb37c5b79529921b99f3df443845817a86de595106cecb4f22b65b"],"state_sha256":"ae2bff9eed8e6c4f148652fc2ea17dee25b97e5c0ab1e910bf46e32cada6609b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MHZAQU2fMqq7QdQupXr3BUZkAh/D79v3sviraTxghKIVSIWTOjzj6zmrbfM9zErUCv1BW1jEgMrhLBFtEydgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T02:16:44.975490Z","bundle_sha256":"7bbe1e902df166d88824ed8aa1a15242b5293c6b86cb847c8e2f4e9f192e19ed"}}