{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:TJNDLY7FVI4SD4XYMS7JHQXSQS","short_pith_number":"pith:TJNDLY7F","canonical_record":{"source":{"id":"0801.3648","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-23T19:24:40Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"de9cb2f6fd8ebea374a6e58b8d02caada20ad1ce08b616d46183fbaf9fb4b2bf","abstract_canon_sha256":"0e11509dc6e554ca27e53a54503c29c6e4d82888dbf64555068fe1056bf72748"},"schema_version":"1.0"},"canonical_sha256":"9a5a35e3e5aa3921f2f864be93c2f284b61e05a12b91872c503c33438a177625","source":{"kind":"arxiv","id":"0801.3648","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3648","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3648v3","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3648","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"TJNDLY7FVI4S","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"TJNDLY7FVI4SD4XY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"TJNDLY7F","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:TJNDLY7FVI4SD4XYMS7JHQXSQS","target":"record","payload":{"canonical_record":{"source":{"id":"0801.3648","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-23T19:24:40Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"de9cb2f6fd8ebea374a6e58b8d02caada20ad1ce08b616d46183fbaf9fb4b2bf","abstract_canon_sha256":"0e11509dc6e554ca27e53a54503c29c6e4d82888dbf64555068fe1056bf72748"},"schema_version":"1.0"},"canonical_sha256":"9a5a35e3e5aa3921f2f864be93c2f284b61e05a12b91872c503c33438a177625","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:57.633826Z","signature_b64":"wQg355KqvJSPqasRXdlwbjiHHAPk2Wn1FGwiIjPEG3kkcvF0VYMyudE9zvdPEqyHq0Ah8xJROLVwU1IkRB6WCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a5a35e3e5aa3921f2f864be93c2f284b61e05a12b91872c503c33438a177625","last_reissued_at":"2026-05-18T02:24:57.633089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:57.633089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.3648","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0+C5PNEIkaBPx2Ew2OWY7uYXj6Tc0XfDwP8grEk+s05xeQFOjkjRNbTz0QhXRURXp9ez9rY/Veb5qZ3mU2WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:16:44.409457Z"},"content_sha256":"c7dd2c8316fb89ed9cae3f9dfc57d62a816e7f8ac550d5454ff6ddce21ea59ef","schema_version":"1.0","event_id":"sha256:c7dd2c8316fb89ed9cae3f9dfc57d62a816e7f8ac550d5454ff6ddce21ea59ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:TJNDLY7FVI4SD4XYMS7JHQXSQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding Rational Periodic Points on Wehler K3 Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Benjamin Hutz","submitted_at":"2008-01-23T19:24:40Z","abstract_excerpt":"This article examines dynamical systems on a class of K3 surfaces in $\\mathbb{P}^{2} \\times \\mathbb{P}^{2}$ with an infinite automorphism group.  In particular, this article develops an algorithm to find $\\mathbb{Q}$-rational periodic points using information modulo $p$ for various primes $p$.  The algorithm is applied to exhibit K3 surfaces with $\\mathbb{Q}$-rational periodic points of primitive period $1,...,16$.  A portion of the algorithm is then used to determine the Riemann zeta function modulo 3 of a particular K3 surface and find a family of K3 surfaces with Picard number two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3648","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jwfrrYm4L6bxROjaVnUckstejRPxW0s37FMquVT9RjtyA4p1sP24SirQrOWREf11Zia4375Qkv/Wmua0kjX7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:16:44.409855Z"},"content_sha256":"9ee61ea60b7aba5d723cd77ee1dbc658b823626e0c7f82704e9a67387c5ac1c4","schema_version":"1.0","event_id":"sha256:9ee61ea60b7aba5d723cd77ee1dbc658b823626e0c7f82704e9a67387c5ac1c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS/bundle.json","state_url":"https://pith.science/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS/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":"2026-05-30T20:16:44Z","links":{"resolver":"https://pith.science/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS","bundle":"https://pith.science/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS/bundle.json","state":"https://pith.science/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJNDLY7FVI4SD4XYMS7JHQXSQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:TJNDLY7FVI4SD4XYMS7JHQXSQS","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":"0e11509dc6e554ca27e53a54503c29c6e4d82888dbf64555068fe1056bf72748","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-23T19:24:40Z","title_canon_sha256":"de9cb2f6fd8ebea374a6e58b8d02caada20ad1ce08b616d46183fbaf9fb4b2bf"},"schema_version":"1.0","source":{"id":"0801.3648","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3648","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3648v3","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3648","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"TJNDLY7FVI4S","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"TJNDLY7FVI4SD4XY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"TJNDLY7F","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:9ee61ea60b7aba5d723cd77ee1dbc658b823626e0c7f82704e9a67387c5ac1c4","target":"graph","created_at":"2026-05-18T02:24:57Z","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":"This article examines dynamical systems on a class of K3 surfaces in $\\mathbb{P}^{2} \\times \\mathbb{P}^{2}$ with an infinite automorphism group.  In particular, this article develops an algorithm to find $\\mathbb{Q}$-rational periodic points using information modulo $p$ for various primes $p$.  The algorithm is applied to exhibit K3 surfaces with $\\mathbb{Q}$-rational periodic points of primitive period $1,...,16$.  A portion of the algorithm is then used to determine the Riemann zeta function modulo 3 of a particular K3 surface and find a family of K3 surfaces with Picard number two.","authors_text":"Benjamin Hutz","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-23T19:24:40Z","title":"Finding Rational Periodic Points on Wehler K3 Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3648","kind":"arxiv","version":3},"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:c7dd2c8316fb89ed9cae3f9dfc57d62a816e7f8ac550d5454ff6ddce21ea59ef","target":"record","created_at":"2026-05-18T02:24:57Z","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":"0e11509dc6e554ca27e53a54503c29c6e4d82888dbf64555068fe1056bf72748","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-01-23T19:24:40Z","title_canon_sha256":"de9cb2f6fd8ebea374a6e58b8d02caada20ad1ce08b616d46183fbaf9fb4b2bf"},"schema_version":"1.0","source":{"id":"0801.3648","kind":"arxiv","version":3}},"canonical_sha256":"9a5a35e3e5aa3921f2f864be93c2f284b61e05a12b91872c503c33438a177625","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a5a35e3e5aa3921f2f864be93c2f284b61e05a12b91872c503c33438a177625","first_computed_at":"2026-05-18T02:24:57.633089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:57.633089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wQg355KqvJSPqasRXdlwbjiHHAPk2Wn1FGwiIjPEG3kkcvF0VYMyudE9zvdPEqyHq0Ah8xJROLVwU1IkRB6WCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:57.633826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.3648","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7dd2c8316fb89ed9cae3f9dfc57d62a816e7f8ac550d5454ff6ddce21ea59ef","sha256:9ee61ea60b7aba5d723cd77ee1dbc658b823626e0c7f82704e9a67387c5ac1c4"],"state_sha256":"51a5100d6c716a81ce35baeb01acae128bc892c39ebe17fdee3979844bfe5f03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmLLbibYOw4LfS6V8qfI5KoH9yxX6URznK73FVePurl/EGRSmAEmAXAF8MFQzsgBnI6nMqd8sD1lT4yGmj3SDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:16:44.411873Z","bundle_sha256":"b064a12197fe5145b24e1a7b4111d067e2b9d1672337b90d1faa985f8a503c5d"}}