{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:65WD3K6QEMWJLOHG7CQ5GL4ZH7","short_pith_number":"pith:65WD3K6Q","canonical_record":{"source":{"id":"1111.2483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T14:26:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"df6c2cd90aa4070e719e0965e6efe6ea97f77a3da6c69fbf73862ca32f74456a","abstract_canon_sha256":"b6eb1d8de37dcdb21b63a1c0a1b6dba0d088ca4322bb22e5baf4018abfa1d26d"},"schema_version":"1.0"},"canonical_sha256":"f76c3dabd0232c95b8e6f8a1d32f993fc8adfe1fa855433513fcfa481d96cf36","source":{"kind":"arxiv","id":"1111.2483","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2483","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2483v2","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2483","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"65WD3K6QEMWJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"65WD3K6QEMWJLOHG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"65WD3K6Q","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:65WD3K6QEMWJLOHG7CQ5GL4ZH7","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T14:26:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"df6c2cd90aa4070e719e0965e6efe6ea97f77a3da6c69fbf73862ca32f74456a","abstract_canon_sha256":"b6eb1d8de37dcdb21b63a1c0a1b6dba0d088ca4322bb22e5baf4018abfa1d26d"},"schema_version":"1.0"},"canonical_sha256":"f76c3dabd0232c95b8e6f8a1d32f993fc8adfe1fa855433513fcfa481d96cf36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:02.333300Z","signature_b64":"z20X+PFMrc+cvb+9MbHOhRtvGEn8bLBE+4NPNyNaB4g1Q+P4XugBvH7W1HC0P0JHy3+WJ0ucsKROotU3m+oYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f76c3dabd0232c95b8e6f8a1d32f993fc8adfe1fa855433513fcfa481d96cf36","last_reissued_at":"2026-05-18T03:07:02.332847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:02.332847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2483","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHBmKR8djdMEyEgbygBmwV+sE0UL2t2Gg/dWxE6EFCSt6vH0vjDiflRykrn3EOhgfU5lkJ3V4CV/ovbPXrZ6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T13:11:26.603451Z"},"content_sha256":"6ec0c1d293a0ec70b93feb939ffa2d60423eeae255e72550e5c7f9ddb1eb804a","schema_version":"1.0","event_id":"sha256:6ec0c1d293a0ec70b93feb939ffa2d60423eeae255e72550e5c7f9ddb1eb804a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:65WD3K6QEMWJLOHG7CQ5GL4ZH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing isomorphism numbers of F-crystals by using level torsions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Xiao Xiao","submitted_at":"2011-11-10T14:26:45Z","abstract_excerpt":"The isomorphism number of an $F$-crystal $(M, \\phi)$ over an algebraically closed field of positive characteristic is the smallest non-negative integer $n_M$ such that the $n_M$-th level truncation of $(M, \\phi)$ determines the isomorphism class of $(M, \\phi)$. When $(M, \\phi)$ is isoclinic, namely it has a unique Newton slopes $\\lambda$, we provide an efficiently computable upper bound of $n_M$ in terms of the Hodge slopes of $(M, \\phi)$ and $\\lambda$. This is achieved by providing an upper bound of the level torsion of $(M, \\phi)$ introduced by Vasiu. We also check that this upper bound is o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2483","kind":"arxiv","version":2},"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":"2026-05-18T03:07:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/5WveqruoukQGlJlqYpxpjP4nqij9O5OmdMMSbW5/etR73skiA9SYK7zVikQVQwN0AEcbn+Jtij57WlyPHXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T13:11:26.603905Z"},"content_sha256":"c10d55133f01290a7dda3a9f65622a5a2bd7bc79f83d77c4496cf0353cbfcef9","schema_version":"1.0","event_id":"sha256:c10d55133f01290a7dda3a9f65622a5a2bd7bc79f83d77c4496cf0353cbfcef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7/bundle.json","state_url":"https://pith.science/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7/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":"2026-08-23T13:11:26Z","links":{"resolver":"https://pith.science/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7","bundle":"https://pith.science/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7/bundle.json","state":"https://pith.science/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/65WD3K6QEMWJLOHG7CQ5GL4ZH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:65WD3K6QEMWJLOHG7CQ5GL4ZH7","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":"b6eb1d8de37dcdb21b63a1c0a1b6dba0d088ca4322bb22e5baf4018abfa1d26d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T14:26:45Z","title_canon_sha256":"df6c2cd90aa4070e719e0965e6efe6ea97f77a3da6c69fbf73862ca32f74456a"},"schema_version":"1.0","source":{"id":"1111.2483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2483","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2483v2","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2483","created_at":"2026-05-18T03:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"65WD3K6QEMWJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"65WD3K6QEMWJLOHG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"65WD3K6Q","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:c10d55133f01290a7dda3a9f65622a5a2bd7bc79f83d77c4496cf0353cbfcef9","target":"graph","created_at":"2026-05-18T03:07:02Z","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":"The isomorphism number of an $F$-crystal $(M, \\phi)$ over an algebraically closed field of positive characteristic is the smallest non-negative integer $n_M$ such that the $n_M$-th level truncation of $(M, \\phi)$ determines the isomorphism class of $(M, \\phi)$. When $(M, \\phi)$ is isoclinic, namely it has a unique Newton slopes $\\lambda$, we provide an efficiently computable upper bound of $n_M$ in terms of the Hodge slopes of $(M, \\phi)$ and $\\lambda$. This is achieved by providing an upper bound of the level torsion of $(M, \\phi)$ introduced by Vasiu. We also check that this upper bound is o","authors_text":"Xiao Xiao","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T14:26:45Z","title":"Computing isomorphism numbers of F-crystals by using level torsions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2483","kind":"arxiv","version":2},"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":"sha256:6ec0c1d293a0ec70b93feb939ffa2d60423eeae255e72550e5c7f9ddb1eb804a","target":"record","created_at":"2026-05-18T03:07:02Z","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":"b6eb1d8de37dcdb21b63a1c0a1b6dba0d088ca4322bb22e5baf4018abfa1d26d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T14:26:45Z","title_canon_sha256":"df6c2cd90aa4070e719e0965e6efe6ea97f77a3da6c69fbf73862ca32f74456a"},"schema_version":"1.0","source":{"id":"1111.2483","kind":"arxiv","version":2}},"canonical_sha256":"f76c3dabd0232c95b8e6f8a1d32f993fc8adfe1fa855433513fcfa481d96cf36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f76c3dabd0232c95b8e6f8a1d32f993fc8adfe1fa855433513fcfa481d96cf36","first_computed_at":"2026-05-18T03:07:02.332847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:02.332847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z20X+PFMrc+cvb+9MbHOhRtvGEn8bLBE+4NPNyNaB4g1Q+P4XugBvH7W1HC0P0JHy3+WJ0ucsKROotU3m+oYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:02.333300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ec0c1d293a0ec70b93feb939ffa2d60423eeae255e72550e5c7f9ddb1eb804a","sha256:c10d55133f01290a7dda3a9f65622a5a2bd7bc79f83d77c4496cf0353cbfcef9"],"state_sha256":"dc509e462f659b536c9d15eabada5d295bcfd21a9c1cd756ca0a3c46f87b11d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pw6ZVENV49keIFP4w8yUFPgrsaHz76tQDGn3eznM4SMoyAAQasYBHKFcDnp1alMJ3rbH93m17tqfNQwJZ7m0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T13:11:26.608677Z","bundle_sha256":"cd9def5f055de102a735b879547c362dd21a5db77e36c2d25bd7cb0831de3547"}}