{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TJTACLRFTBJAB4HPPXC4BLDZGT","short_pith_number":"pith:TJTACLRF","canonical_record":{"source":{"id":"1602.06608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T00:02:55Z","cross_cats_sorted":[],"title_canon_sha256":"3ced7079ce915dde8da152ef543478520811a79607c542b65cb55f81eae3313e","abstract_canon_sha256":"ef533a8f271f384511852071e25f89912bf0fc60cd6f80da0c1b5bf4240ef9fc"},"schema_version":"1.0"},"canonical_sha256":"9a66012e25985200f0ef7dc5c0ac7934d28171101c8976ccdb8940454505d551","source":{"kind":"arxiv","id":"1602.06608","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06608","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06608v1","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06608","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"TJTACLRFTBJA","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TJTACLRFTBJAB4HP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TJTACLRF","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TJTACLRFTBJAB4HPPXC4BLDZGT","target":"record","payload":{"canonical_record":{"source":{"id":"1602.06608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T00:02:55Z","cross_cats_sorted":[],"title_canon_sha256":"3ced7079ce915dde8da152ef543478520811a79607c542b65cb55f81eae3313e","abstract_canon_sha256":"ef533a8f271f384511852071e25f89912bf0fc60cd6f80da0c1b5bf4240ef9fc"},"schema_version":"1.0"},"canonical_sha256":"9a66012e25985200f0ef7dc5c0ac7934d28171101c8976ccdb8940454505d551","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:17.078699Z","signature_b64":"m4a+cRWzERSckNaY7te1sjwGX2Z2CMtlDQsHpJ4uRU0eaUnylS5OyoP/X61HEAURW//2p0MLZ1k2go9yC4PzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a66012e25985200f0ef7dc5c0ac7934d28171101c8976ccdb8940454505d551","last_reissued_at":"2026-05-17T23:54:17.078270Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:17.078270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.06608","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":"2026-05-17T23:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lS30j8wE1TTFtAjh7Id1Go9W+2bwpYACijLq3CoJMXqVLsx2Z8gptQuxxobTbm1YaA6IWNJBkMOzIYueBWeLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:20:34.677482Z"},"content_sha256":"25a9922a6647214d5c9919e340dffb95ca33fce8e3811122446a050ba82e7d2b","schema_version":"1.0","event_id":"sha256:25a9922a6647214d5c9919e340dffb95ca33fce8e3811122446a050ba82e7d2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TJTACLRFTBJAB4HPPXC4BLDZGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of infinite, non-trivial $F$-sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Ferraguti, Giacomo Micheli","submitted_at":"2016-02-22T00:02:55Z","abstract_excerpt":"In this paper we prove a conjecture of J. Andrade, S. J. Miller, K. Pratt and M. Trinh, showing the existence of a non trivial infinite $F$-set over $\\mathbb F_q[x]$ for every fixed $q$. We also provide the proof of a refinement of the conjecture, involving the notion of width of an $F$-set, which is a natural number encoding the complexity of the set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06608","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":""},"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":"2026-05-17T23:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MrHyZfkIiztpPAW1s1B64PwqX/o/zoD8I+zkxdGbmT6lk/BojBpqwfqj8xsbDrRmFUPJJmYZzk40IvYhWEJVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:20:34.677819Z"},"content_sha256":"2d5fdfca3a417b45043c191ef7ebeee0ecc761e9835983012ab975392e38373d","schema_version":"1.0","event_id":"sha256:2d5fdfca3a417b45043c191ef7ebeee0ecc761e9835983012ab975392e38373d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJTACLRFTBJAB4HPPXC4BLDZGT/bundle.json","state_url":"https://pith.science/pith/TJTACLRFTBJAB4HPPXC4BLDZGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJTACLRFTBJAB4HPPXC4BLDZGT/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":"2026-06-24T19:20:34Z","links":{"resolver":"https://pith.science/pith/TJTACLRFTBJAB4HPPXC4BLDZGT","bundle":"https://pith.science/pith/TJTACLRFTBJAB4HPPXC4BLDZGT/bundle.json","state":"https://pith.science/pith/TJTACLRFTBJAB4HPPXC4BLDZGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJTACLRFTBJAB4HPPXC4BLDZGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TJTACLRFTBJAB4HPPXC4BLDZGT","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":"ef533a8f271f384511852071e25f89912bf0fc60cd6f80da0c1b5bf4240ef9fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T00:02:55Z","title_canon_sha256":"3ced7079ce915dde8da152ef543478520811a79607c542b65cb55f81eae3313e"},"schema_version":"1.0","source":{"id":"1602.06608","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06608","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06608v1","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06608","created_at":"2026-05-17T23:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"TJTACLRFTBJA","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TJTACLRFTBJAB4HP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TJTACLRF","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:2d5fdfca3a417b45043c191ef7ebeee0ecc761e9835983012ab975392e38373d","target":"graph","created_at":"2026-05-17T23:54:17Z","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":"In this paper we prove a conjecture of J. Andrade, S. J. Miller, K. Pratt and M. Trinh, showing the existence of a non trivial infinite $F$-set over $\\mathbb F_q[x]$ for every fixed $q$. We also provide the proof of a refinement of the conjecture, involving the notion of width of an $F$-set, which is a natural number encoding the complexity of the set.","authors_text":"Andrea Ferraguti, Giacomo Micheli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T00:02:55Z","title":"On the existence of infinite, non-trivial $F$-sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06608","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":"sha256:25a9922a6647214d5c9919e340dffb95ca33fce8e3811122446a050ba82e7d2b","target":"record","created_at":"2026-05-17T23:54:17Z","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":"ef533a8f271f384511852071e25f89912bf0fc60cd6f80da0c1b5bf4240ef9fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-22T00:02:55Z","title_canon_sha256":"3ced7079ce915dde8da152ef543478520811a79607c542b65cb55f81eae3313e"},"schema_version":"1.0","source":{"id":"1602.06608","kind":"arxiv","version":1}},"canonical_sha256":"9a66012e25985200f0ef7dc5c0ac7934d28171101c8976ccdb8940454505d551","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a66012e25985200f0ef7dc5c0ac7934d28171101c8976ccdb8940454505d551","first_computed_at":"2026-05-17T23:54:17.078270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:17.078270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m4a+cRWzERSckNaY7te1sjwGX2Z2CMtlDQsHpJ4uRU0eaUnylS5OyoP/X61HEAURW//2p0MLZ1k2go9yC4PzBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:17.078699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06608","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25a9922a6647214d5c9919e340dffb95ca33fce8e3811122446a050ba82e7d2b","sha256:2d5fdfca3a417b45043c191ef7ebeee0ecc761e9835983012ab975392e38373d"],"state_sha256":"a7a4bc30a2bc78f0fc4a947330e26d61dd20fa4dd1a4e2c744028be945939dcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PmW0wSX2zAD6GYDgPHCA4K5f6TyrelthuOUUl5hAYF+odjRcneYaHwz1V6FYG0vqc7unZMqeUw5pKnb/J8yQCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:20:34.679882Z","bundle_sha256":"ac099c80d95f9dd6062b6013d3497173977d864dbe462ab6179eb2bf61970173"}}