{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:J4RXHKECTLEOP6OU2OAWDE2LY7","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":"e2a905eddb336537a4efb88ac54cf1793cfaeeebedc03ca2e28c61c303d42395","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-27T09:40:21Z","title_canon_sha256":"f57b909a5c2ed606320012d7cfa9ac7ac6f668399346cc81eca72d7f5d01c4fd"},"schema_version":"1.0","source":{"id":"0806.4469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4469","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4469v1","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4469","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"J4RXHKECTLEO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"J4RXHKECTLEOP6OU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"J4RXHKEC","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:76108f830c84bf97bbc2df6c16cecadd278055412168f7547e942dca1ecdcfe6","target":"graph","created_at":"2026-05-18T04:40:46Z","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":"To a definable subset of Z_p^n (or to a scheme of finite type over Z_p) one can associate a tree in a natural way. It is known that the corresponding Poincare series P(X) = \\sum_i N_i X^i is rational, where N_i is the number of nodes of the tree at depth i. This suggests that the trees themselves are far from arbitrary. We state a conjectural, purely combinatorial description of the class of possible trees and provide some evidence for it. We verify that any tree in our class indeed arises from a definable set, and we prove that the tree of a definable set (or of a scheme) lies in our class in","authors_text":"Immanuel Halupczok","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-27T09:40:21Z","title":"Trees of definable sets over the p-adics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4469","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":"sha256:39b79e696464ae93b2ebad04d5cad9ed8728991e9bc92d03c322cf3f34689773","target":"record","created_at":"2026-05-18T04:40:46Z","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":"e2a905eddb336537a4efb88ac54cf1793cfaeeebedc03ca2e28c61c303d42395","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-06-27T09:40:21Z","title_canon_sha256":"f57b909a5c2ed606320012d7cfa9ac7ac6f668399346cc81eca72d7f5d01c4fd"},"schema_version":"1.0","source":{"id":"0806.4469","kind":"arxiv","version":1}},"canonical_sha256":"4f2373a8829ac8e7f9d4d38161934bc7c931beae761dd834ba9f6bba612296ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f2373a8829ac8e7f9d4d38161934bc7c931beae761dd834ba9f6bba612296ef","first_computed_at":"2026-05-18T04:40:46.565786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:46.565786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Lz2HtzHjsn8gGwaJcCXAPokP9RxYLzG6ZGbKWZfD3LT0qEmJrNz7slaYJGJBHTRvSWMDLkzPxwSSkxVYHP1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:46.566278Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39b79e696464ae93b2ebad04d5cad9ed8728991e9bc92d03c322cf3f34689773","sha256:76108f830c84bf97bbc2df6c16cecadd278055412168f7547e942dca1ecdcfe6"],"state_sha256":"12a2bec34df075f2d3a0ccf09030b1d2df06f5dc907b44c8814fa70077989a75"}