{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:E7U476JWTRR2F2DGLOYICCFR2Y","short_pith_number":"pith:E7U476JW","canonical_record":{"source":{"id":"1908.04775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-13T17:41:17Z","cross_cats_sorted":["math.MG","math.NT","math.PR"],"title_canon_sha256":"3526fa96ba555d617b6072f5aef6dbc8aa0ea5d2905b99dee907d3085c7a9b80","abstract_canon_sha256":"d16909d03332b6e335cb03017f9562abdbc279e5759c56e825442e6b056f6042"},"schema_version":"1.0"},"canonical_sha256":"27e9cff9369c63a2e8665bb08108b1d60bbcf0ebb76900b607249e0d007ea1d1","source":{"kind":"arxiv","id":"1908.04775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04775","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04775v1","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04775","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"E7U476JWTRR2","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"pith_short_16","alias_value":"E7U476JWTRR2F2DG","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"pith_short_8","alias_value":"E7U476JW","created_at":"2026-07-04T23:55:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:E7U476JWTRR2F2DGLOYICCFR2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-13T17:41:17Z","cross_cats_sorted":["math.MG","math.NT","math.PR"],"title_canon_sha256":"3526fa96ba555d617b6072f5aef6dbc8aa0ea5d2905b99dee907d3085c7a9b80","abstract_canon_sha256":"d16909d03332b6e335cb03017f9562abdbc279e5759c56e825442e6b056f6042"},"schema_version":"1.0"},"canonical_sha256":"27e9cff9369c63a2e8665bb08108b1d60bbcf0ebb76900b607249e0d007ea1d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:55:16.434344Z","signature_b64":"B41pw4xhY2sRF8b1D6lf6iPkbnBvwywFXLr9MPijHuqO+n1iFe2IC2ZdLS2DZpGIAtcDEBhcRfBQ47RVh9x0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27e9cff9369c63a2e8665bb08108b1d60bbcf0ebb76900b607249e0d007ea1d1","last_reissued_at":"2026-07-04T23:55:16.433942Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:55:16.433942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04775","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":"2026-07-04T23:55:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aE/Fj7ZVkeWuPKY4fkR6OyHKckGWKgNEA0K3dsu0BV0JWyz9J9XAlFjchAB27jpI6tLbGZGeqNrT7Psr2EOFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:07:33.793569Z"},"content_sha256":"97c97cde5766bde32285909b62bf432a5eaff54cc565f4ce3d96067c6ce815d7","schema_version":"1.0","event_id":"sha256:97c97cde5766bde32285909b62bf432a5eaff54cc565f4ce3d96067c6ce815d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:E7U476JWTRR2F2DGLOYICCFR2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-adic Integral Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT","math.PR"],"primary_cat":"math.AG","authors_text":"Antonio Lerario, Avinash Kulkarni","submitted_at":"2019-08-13T17:41:17Z","abstract_excerpt":"We prove a $p$-adic version of the Integral Geometry Formula for averaging the intersection of two $p$-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective set (reproving a result by Oesterl\\'e) and to the study of random $p$-adic polynomial systems of equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04775","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/1908.04775/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":"2026-07-04T23:55:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14S1hWRSHFLIJWWQGuSVRmkqIPrU7U5XL9wnkmaloqxGTzNdcJLUfXnjHVQqGDZ+v6BbiAUObz3rEA4FfgQABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:07:33.794079Z"},"content_sha256":"a9bbe310bfa31a41f2016d6cf964491f03c84f744e74f8f784e1be62f3dcdd67","schema_version":"1.0","event_id":"sha256:a9bbe310bfa31a41f2016d6cf964491f03c84f744e74f8f784e1be62f3dcdd67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7U476JWTRR2F2DGLOYICCFR2Y/bundle.json","state_url":"https://pith.science/pith/E7U476JWTRR2F2DGLOYICCFR2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7U476JWTRR2F2DGLOYICCFR2Y/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":"2026-08-16T13:07:33Z","links":{"resolver":"https://pith.science/pith/E7U476JWTRR2F2DGLOYICCFR2Y","bundle":"https://pith.science/pith/E7U476JWTRR2F2DGLOYICCFR2Y/bundle.json","state":"https://pith.science/pith/E7U476JWTRR2F2DGLOYICCFR2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7U476JWTRR2F2DGLOYICCFR2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:E7U476JWTRR2F2DGLOYICCFR2Y","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":"d16909d03332b6e335cb03017f9562abdbc279e5759c56e825442e6b056f6042","cross_cats_sorted":["math.MG","math.NT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-13T17:41:17Z","title_canon_sha256":"3526fa96ba555d617b6072f5aef6dbc8aa0ea5d2905b99dee907d3085c7a9b80"},"schema_version":"1.0","source":{"id":"1908.04775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04775","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04775v1","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04775","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"E7U476JWTRR2","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"pith_short_16","alias_value":"E7U476JWTRR2F2DG","created_at":"2026-07-04T23:55:16Z"},{"alias_kind":"pith_short_8","alias_value":"E7U476JW","created_at":"2026-07-04T23:55:16Z"}],"graph_snapshots":[{"event_id":"sha256:a9bbe310bfa31a41f2016d6cf964491f03c84f744e74f8f784e1be62f3dcdd67","target":"graph","created_at":"2026-07-04T23:55:16Z","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/1908.04775/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a $p$-adic version of the Integral Geometry Formula for averaging the intersection of two $p$-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective set (reproving a result by Oesterl\\'e) and to the study of random $p$-adic polynomial systems of equations.","authors_text":"Antonio Lerario, Avinash Kulkarni","cross_cats":["math.MG","math.NT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-13T17:41:17Z","title":"$p$-adic Integral Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04775","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":"sha256:97c97cde5766bde32285909b62bf432a5eaff54cc565f4ce3d96067c6ce815d7","target":"record","created_at":"2026-07-04T23:55:16Z","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":"d16909d03332b6e335cb03017f9562abdbc279e5759c56e825442e6b056f6042","cross_cats_sorted":["math.MG","math.NT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-13T17:41:17Z","title_canon_sha256":"3526fa96ba555d617b6072f5aef6dbc8aa0ea5d2905b99dee907d3085c7a9b80"},"schema_version":"1.0","source":{"id":"1908.04775","kind":"arxiv","version":1}},"canonical_sha256":"27e9cff9369c63a2e8665bb08108b1d60bbcf0ebb76900b607249e0d007ea1d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27e9cff9369c63a2e8665bb08108b1d60bbcf0ebb76900b607249e0d007ea1d1","first_computed_at":"2026-07-04T23:55:16.433942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:16.433942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B41pw4xhY2sRF8b1D6lf6iPkbnBvwywFXLr9MPijHuqO+n1iFe2IC2ZdLS2DZpGIAtcDEBhcRfBQ47RVh9x0Bg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:16.434344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97c97cde5766bde32285909b62bf432a5eaff54cc565f4ce3d96067c6ce815d7","sha256:a9bbe310bfa31a41f2016d6cf964491f03c84f744e74f8f784e1be62f3dcdd67"],"state_sha256":"3ae67063680d6781b23892c6ab20c2e0574b33df6b0d236c06701d3d8f72db4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9I40ioj5wn2x5xZV6ufEDS8Lzr5ehVE3WMJj/7h9aLanq19gYQwRao+ALUCclRhYHQM1wRcGFGk469zRredsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:07:33.798111Z","bundle_sha256":"53496f4877d40cfc6f5dc20fce6f0998c3f2355c1a13e0e8c5f0301c78f41acd"}}