{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:Y5UX4V7K4UJ4SZY7IXDQPFM2BC","short_pith_number":"pith:Y5UX4V7K","canonical_record":{"source":{"id":"math/0508364","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-08-19T02:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"1c793f64d07937b3059214fcd60ee71fe08ff6ed4c74c7279c3b90aa284ee210","abstract_canon_sha256":"3f1b60c883346f16535deb11da175e2ed22fac250502efb4082f8baa5ade9f6e"},"schema_version":"1.0"},"canonical_sha256":"c7697e57eae513c9671f45c707959a0893e4a6bfe5250f78eebe90755c68e7d4","source":{"kind":"arxiv","id":"math/0508364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508364","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508364v1","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508364","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"Y5UX4V7K4UJ4","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"pith_short_16","alias_value":"Y5UX4V7K4UJ4SZY7","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"pith_short_8","alias_value":"Y5UX4V7K","created_at":"2026-07-04T14:40:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:Y5UX4V7K4UJ4SZY7IXDQPFM2BC","target":"record","payload":{"canonical_record":{"source":{"id":"math/0508364","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-08-19T02:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"1c793f64d07937b3059214fcd60ee71fe08ff6ed4c74c7279c3b90aa284ee210","abstract_canon_sha256":"3f1b60c883346f16535deb11da175e2ed22fac250502efb4082f8baa5ade9f6e"},"schema_version":"1.0"},"canonical_sha256":"c7697e57eae513c9671f45c707959a0893e4a6bfe5250f78eebe90755c68e7d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:19.030986Z","signature_b64":"zFCXRgLoeN0XAKlOJj1KJDj2B53KrxfWG5IisRePlemp6V/WJXYmkjaZ3mqcPheufGaX/+aAJ6fRoRrMTPPCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7697e57eae513c9671f45c707959a0893e4a6bfe5250f78eebe90755c68e7d4","last_reissued_at":"2026-07-04T14:40:19.030602Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:19.030602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0508364","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":"2026-07-04T14:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qiSoI5+LE8cVDMZvHPty4hW+dd2QC/Fgo1Ajk6srrV+VcR9bvtoirAw5DyJRv9i+7wqchfg9vcGVO6fRsOsoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:41:27.409465Z"},"content_sha256":"e36b10316024180d29d11b255127a6ff11ae8ea1f3a301ec85e06bca188111d9","schema_version":"1.0","event_id":"sha256:e36b10316024180d29d11b255127a6ff11ae8ea1f3a301ec85e06bca188111d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:Y5UX4V7K4UJ4SZY7IXDQPFM2BC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Number Derivatives","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Stay","submitted_at":"2005-08-19T02:54:04Z","abstract_excerpt":"We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to examine some of its basic properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508364","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0508364/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WIWRevLXX/ilGrcFP0/mEwPVUNdsaljzEM0y1N0Cuf92MG1bLFhp7W+wsc8G2RPuS1I89mm+FrNboMUW42nZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:41:27.409843Z"},"content_sha256":"0fe16effc8b7fb45be4a675a30fe8f0cb3831a16f89ffa25e9477b9154827a2f","schema_version":"1.0","event_id":"sha256:0fe16effc8b7fb45be4a675a30fe8f0cb3831a16f89ffa25e9477b9154827a2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC/bundle.json","state_url":"https://pith.science/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC/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":"2026-07-04T18:41:27Z","links":{"resolver":"https://pith.science/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC","bundle":"https://pith.science/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC/bundle.json","state":"https://pith.science/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5UX4V7K4UJ4SZY7IXDQPFM2BC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:Y5UX4V7K4UJ4SZY7IXDQPFM2BC","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":"3f1b60c883346f16535deb11da175e2ed22fac250502efb4082f8baa5ade9f6e","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-08-19T02:54:04Z","title_canon_sha256":"1c793f64d07937b3059214fcd60ee71fe08ff6ed4c74c7279c3b90aa284ee210"},"schema_version":"1.0","source":{"id":"math/0508364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508364","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508364v1","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508364","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"Y5UX4V7K4UJ4","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"pith_short_16","alias_value":"Y5UX4V7K4UJ4SZY7","created_at":"2026-07-04T14:40:19Z"},{"alias_kind":"pith_short_8","alias_value":"Y5UX4V7K","created_at":"2026-07-04T14:40:19Z"}],"graph_snapshots":[{"event_id":"sha256:0fe16effc8b7fb45be4a675a30fe8f0cb3831a16f89ffa25e9477b9154827a2f","target":"graph","created_at":"2026-07-04T14:40:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0508364/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to examine some of its basic properties.","authors_text":"Michael Stay","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-08-19T02:54:04Z","title":"Generalized Number Derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508364","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:e36b10316024180d29d11b255127a6ff11ae8ea1f3a301ec85e06bca188111d9","target":"record","created_at":"2026-07-04T14:40:19Z","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":"3f1b60c883346f16535deb11da175e2ed22fac250502efb4082f8baa5ade9f6e","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-08-19T02:54:04Z","title_canon_sha256":"1c793f64d07937b3059214fcd60ee71fe08ff6ed4c74c7279c3b90aa284ee210"},"schema_version":"1.0","source":{"id":"math/0508364","kind":"arxiv","version":1}},"canonical_sha256":"c7697e57eae513c9671f45c707959a0893e4a6bfe5250f78eebe90755c68e7d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7697e57eae513c9671f45c707959a0893e4a6bfe5250f78eebe90755c68e7d4","first_computed_at":"2026-07-04T14:40:19.030602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:19.030602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zFCXRgLoeN0XAKlOJj1KJDj2B53KrxfWG5IisRePlemp6V/WJXYmkjaZ3mqcPheufGaX/+aAJ6fRoRrMTPPCDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:19.030986Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e36b10316024180d29d11b255127a6ff11ae8ea1f3a301ec85e06bca188111d9","sha256:0fe16effc8b7fb45be4a675a30fe8f0cb3831a16f89ffa25e9477b9154827a2f"],"state_sha256":"13dacd9ee1a03c04120691fb8ce1148cd882f684bb458b0bc175d71020e9e4f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ypV8dRRy2qQvm6yU2a60EJKfQjuT2Wm60izmev/SLkPsM6xr7ZezGciamH5/EFxtzhP+0bj1k50I+VC45v9MBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:41:27.411974Z","bundle_sha256":"a1b952d4d9b676eca9d5e1a7152bd533009ae30d34fd71d7f8a2f8e2f2247fe2"}}