{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LJ5K4QPFE2AHBMOGOVML4P32OG","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":"11cfd467932c23a784b027cb9e7215068c674f5e8351cd28dd62e15d3e7b0b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-05-18T15:04:53Z","title_canon_sha256":"e1ad0dcb1a3bb36db30296a8d458210ce6d4fc8a7ad0779b9e09a838092cd02c"},"schema_version":"1.0","source":{"id":"1205.4170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4170","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4170v1","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4170","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"LJ5K4QPFE2AH","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LJ5K4QPFE2AHBMOG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LJ5K4QPF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:ee2417ee5f54172812ee8ed52e8c5a86af58af09155461f2ac13ff5a56e818c8","target":"graph","created_at":"2026-05-18T03:55:22Z","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"},"paper":{"abstract_excerpt":"We develop a notion of cell decomposition suitable for studying weak p- adic structures (reducts of p-adic fields where addition and multiplication are not (everywhere) definable). As an example, we apply this to a language with restricted addition.","authors_text":"Eva Leenknegt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-05-18T15:04:53Z","title":"Cell decomposition and definable functions for weak p-adic structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4170","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":"sha256:2a7a57368ee3ad3543baf28e487cbe2e6863212819caebe1ef32ddf308d37fd9","target":"record","created_at":"2026-05-18T03:55:22Z","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":"11cfd467932c23a784b027cb9e7215068c674f5e8351cd28dd62e15d3e7b0b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-05-18T15:04:53Z","title_canon_sha256":"e1ad0dcb1a3bb36db30296a8d458210ce6d4fc8a7ad0779b9e09a838092cd02c"},"schema_version":"1.0","source":{"id":"1205.4170","kind":"arxiv","version":1}},"canonical_sha256":"5a7aae41e5268070b1c67558be3f7a719a3bc21c01a20602b5e05c6bfd5e2496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7aae41e5268070b1c67558be3f7a719a3bc21c01a20602b5e05c6bfd5e2496","first_computed_at":"2026-05-18T03:55:22.571913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:22.571913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bSW4XRDBUs/fEuy8aHyuCBwdRgkFqvS3NvTWQP1R/Rij1AJ498eDujLHQQYX/riTL1YTebeSwBCCC2+a1OoODA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:22.572573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a7a57368ee3ad3543baf28e487cbe2e6863212819caebe1ef32ddf308d37fd9","sha256:ee2417ee5f54172812ee8ed52e8c5a86af58af09155461f2ac13ff5a56e818c8"],"state_sha256":"a6441a6612263ab170963b5793b9d2a7c0d29fda8b9618d28ae3ad7b2aab1d92"}