{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KV2MXJ4VZXYYPV6URD2AQODI3Z","short_pith_number":"pith:KV2MXJ4V","canonical_record":{"source":{"id":"1502.03371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-11T16:56:30Z","cross_cats_sorted":["cs.NA","eess.SP"],"title_canon_sha256":"5a2cf76b4cfae9886075d0389474b5b399499665a327db1479c27bd74aca4327","abstract_canon_sha256":"8fde9c61e25aad1df71b339bf21eb5d987157afdbb0d7f27021e262b6409a3f8"},"schema_version":"1.0"},"canonical_sha256":"5574cba795cdf187d7d488f4083868de7124235c6dd9b2c71062b89e71bae511","source":{"kind":"arxiv","id":"1502.03371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03371","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03371v1","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03371","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"KV2MXJ4VZXYY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KV2MXJ4VZXYYPV6U","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KV2MXJ4V","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KV2MXJ4VZXYYPV6URD2AQODI3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1502.03371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-11T16:56:30Z","cross_cats_sorted":["cs.NA","eess.SP"],"title_canon_sha256":"5a2cf76b4cfae9886075d0389474b5b399499665a327db1479c27bd74aca4327","abstract_canon_sha256":"8fde9c61e25aad1df71b339bf21eb5d987157afdbb0d7f27021e262b6409a3f8"},"schema_version":"1.0"},"canonical_sha256":"5574cba795cdf187d7d488f4083868de7124235c6dd9b2c71062b89e71bae511","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:08.212607Z","signature_b64":"wLufxs3V4vsu2qjdpsLM4cc97ark05nyukEuTID+7zKcJo+T5bEhG6YikRiTC/oeXYQh2WefbT/6ca/FU8DDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5574cba795cdf187d7d488f4083868de7124235c6dd9b2c71062b89e71bae511","last_reissued_at":"2026-05-18T00:25:08.212108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:08.212108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.03371","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":"2026-05-18T00:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfEPzD7ESyATfEFm31sSXdBcEe4tfFUz7bMcbGm0JiEQ8pM6n6/0gseNXwePkfEluST9hgXzdk1tY2vF0ZyvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:41:47.108510Z"},"content_sha256":"9b38f9b35d9ad5ec33739ce5644eb8820abc8f63452f7001b53a1c69942d12d3","schema_version":"1.0","event_id":"sha256:9b38f9b35d9ad5ec33739ce5644eb8820abc8f63452f7001b53a1c69942d12d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KV2MXJ4VZXYYPV6URD2AQODI3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Z Transform over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","eess.SP"],"primary_cat":"math.NT","authors_text":"D. Silva, H.M. de Oliveira, R.M. Campello de Souza","submitted_at":"2015-02-11T16:56:30Z","abstract_excerpt":"Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03371","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":"2026-05-18T00:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ct7jOBC6hKiiKtrwFYBQ+gKsVRKbXxkRbpzz+G6+2akJu2n89s935hCgF9Y2U60CT83fM14bSs6OBlwFyGj2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:41:47.109195Z"},"content_sha256":"a393709c91c3e6ac9d46c5253f5aaf8c78f77b400cb73ef6aa48903f3f351b9c","schema_version":"1.0","event_id":"sha256:a393709c91c3e6ac9d46c5253f5aaf8c78f77b400cb73ef6aa48903f3f351b9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z/bundle.json","state_url":"https://pith.science/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z/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":"2026-06-09T03:41:47Z","links":{"resolver":"https://pith.science/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z","bundle":"https://pith.science/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z/bundle.json","state":"https://pith.science/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KV2MXJ4VZXYYPV6URD2AQODI3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KV2MXJ4VZXYYPV6URD2AQODI3Z","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":"8fde9c61e25aad1df71b339bf21eb5d987157afdbb0d7f27021e262b6409a3f8","cross_cats_sorted":["cs.NA","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-11T16:56:30Z","title_canon_sha256":"5a2cf76b4cfae9886075d0389474b5b399499665a327db1479c27bd74aca4327"},"schema_version":"1.0","source":{"id":"1502.03371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03371","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03371v1","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03371","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"KV2MXJ4VZXYY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KV2MXJ4VZXYYPV6U","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KV2MXJ4V","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:a393709c91c3e6ac9d46c5253f5aaf8c78f77b400cb73ef6aa48903f3f351b9c","target":"graph","created_at":"2026-05-18T00:25:08Z","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":"Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.","authors_text":"D. Silva, H.M. de Oliveira, R.M. Campello de Souza","cross_cats":["cs.NA","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-11T16:56:30Z","title":"The Z Transform over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03371","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":"sha256:9b38f9b35d9ad5ec33739ce5644eb8820abc8f63452f7001b53a1c69942d12d3","target":"record","created_at":"2026-05-18T00:25:08Z","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":"8fde9c61e25aad1df71b339bf21eb5d987157afdbb0d7f27021e262b6409a3f8","cross_cats_sorted":["cs.NA","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-11T16:56:30Z","title_canon_sha256":"5a2cf76b4cfae9886075d0389474b5b399499665a327db1479c27bd74aca4327"},"schema_version":"1.0","source":{"id":"1502.03371","kind":"arxiv","version":1}},"canonical_sha256":"5574cba795cdf187d7d488f4083868de7124235c6dd9b2c71062b89e71bae511","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5574cba795cdf187d7d488f4083868de7124235c6dd9b2c71062b89e71bae511","first_computed_at":"2026-05-18T00:25:08.212108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:08.212108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wLufxs3V4vsu2qjdpsLM4cc97ark05nyukEuTID+7zKcJo+T5bEhG6YikRiTC/oeXYQh2WefbT/6ca/FU8DDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:08.212607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b38f9b35d9ad5ec33739ce5644eb8820abc8f63452f7001b53a1c69942d12d3","sha256:a393709c91c3e6ac9d46c5253f5aaf8c78f77b400cb73ef6aa48903f3f351b9c"],"state_sha256":"9f75af686d362dfd2dfd2c488d1276651dc554505c201dcf9ddd818596a1dc49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9JQTF7qhIGmwUAM4toJL7zBpe0wcdmwfwBkVugD2xRzw8KlK9iGzMHFo2DpKqwGdAT6GxJCoSd/WGIUebO2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:41:47.113003Z","bundle_sha256":"24a6f0fd24165a64dfe05dd51930a9635c0eb706b361b292759c075d3d43726a"}}