{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:UUX2XKQI6VSBFRY2SZDK5ASR5L","short_pith_number":"pith:UUX2XKQI","canonical_record":{"source":{"id":"0711.3659","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2007-11-23T00:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"14894cb6b75d23f160eabc9f06edc34597f9bc3485c47b81e7bf07e8f90977a0","abstract_canon_sha256":"903022b2651f562ecc4fd2357eb97ed4c9602bf425f0645fef18d18b6ec7b6a3"},"schema_version":"1.0"},"canonical_sha256":"a52fabaa08f56412c71a9646ae8251eac4330e6476886a2cdda39af0260e663f","source":{"kind":"arxiv","id":"0711.3659","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3659","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3659v1","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3659","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"UUX2XKQI6VSB","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUX2XKQI6VSBFRY2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUX2XKQI","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:UUX2XKQI6VSBFRY2SZDK5ASR5L","target":"record","payload":{"canonical_record":{"source":{"id":"0711.3659","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2007-11-23T00:55:11Z","cross_cats_sorted":[],"title_canon_sha256":"14894cb6b75d23f160eabc9f06edc34597f9bc3485c47b81e7bf07e8f90977a0","abstract_canon_sha256":"903022b2651f562ecc4fd2357eb97ed4c9602bf425f0645fef18d18b6ec7b6a3"},"schema_version":"1.0"},"canonical_sha256":"a52fabaa08f56412c71a9646ae8251eac4330e6476886a2cdda39af0260e663f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:09.648302Z","signature_b64":"vW6p9X8ErxmTPct5yL7Urjc2xl6sIczvbQXxwa3HNJoL0lb8SblvJgM1BQfR/VnP9beAUZXEWvku/HVqDtHeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a52fabaa08f56412c71a9646ae8251eac4330e6476886a2cdda39af0260e663f","last_reissued_at":"2026-05-18T03:37:09.647567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:09.647567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0711.3659","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":"2026-05-18T03:37:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oo2mYLAKt8+O7B9k4Aj0M44SXU5QaLbB8zXV5tTZ3V/ioRyhwnlwR+G4A3HGNCd3F0lyp5qlG2HgBdasQ/NODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:32:22.190362Z"},"content_sha256":"5cf8bff82105a31aa9289d3b08cf3837447669c066344e75431c8c98fc645143","schema_version":"1.0","event_id":"sha256:5cf8bff82105a31aa9289d3b08cf3837447669c066344e75431c8c98fc645143"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:UUX2XKQI6VSBFRY2SZDK5ASR5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Axiomatics of Ann-Categories","license":"","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"D. D. Hanh, Nguyen Tien Quang, N. T. Thuy","submitted_at":"2007-11-23T00:55:11Z","abstract_excerpt":"In this paper, we have studied the axiomatics of {\\it Ann-categories} and {\\it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have achieved is proving the independence of the axiomatics of Ann-category definition. And then we have proved that after adding an axiom into the definition of categorical rings, we obtain the new axiomatics which is equivalent to the one of Ann-categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3659","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":"2026-05-18T03:37:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ipjHaLXjIH2+wDKxKWyx8hdP/JzoOAa0X4JSniiAVak26sF0/0nIHWfjiTRLOy9LwoZHCnfjok19OcCON6BDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:32:22.190862Z"},"content_sha256":"e0a629449022b970dd43ba0814480f6cdd90c644a7e725886a104f02dd5e51ba","schema_version":"1.0","event_id":"sha256:e0a629449022b970dd43ba0814480f6cdd90c644a7e725886a104f02dd5e51ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L/bundle.json","state_url":"https://pith.science/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L/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":"2026-05-28T00:32:22Z","links":{"resolver":"https://pith.science/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L","bundle":"https://pith.science/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L/bundle.json","state":"https://pith.science/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUX2XKQI6VSBFRY2SZDK5ASR5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UUX2XKQI6VSBFRY2SZDK5ASR5L","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":"903022b2651f562ecc4fd2357eb97ed4c9602bf425f0645fef18d18b6ec7b6a3","cross_cats_sorted":[],"license":"","primary_cat":"math.CT","submitted_at":"2007-11-23T00:55:11Z","title_canon_sha256":"14894cb6b75d23f160eabc9f06edc34597f9bc3485c47b81e7bf07e8f90977a0"},"schema_version":"1.0","source":{"id":"0711.3659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3659","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3659v1","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3659","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"UUX2XKQI6VSB","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUX2XKQI6VSBFRY2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUX2XKQI","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:e0a629449022b970dd43ba0814480f6cdd90c644a7e725886a104f02dd5e51ba","target":"graph","created_at":"2026-05-18T03:37:09Z","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 have studied the axiomatics of {\\it Ann-categories} and {\\it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have achieved is proving the independence of the axiomatics of Ann-category definition. And then we have proved that after adding an axiom into the definition of categorical rings, we obtain the new axiomatics which is equivalent to the one of Ann-categories.","authors_text":"D. D. Hanh, Nguyen Tien Quang, N. T. Thuy","cross_cats":[],"headline":"","license":"","primary_cat":"math.CT","submitted_at":"2007-11-23T00:55:11Z","title":"On the Axiomatics of Ann-Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3659","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":"sha256:5cf8bff82105a31aa9289d3b08cf3837447669c066344e75431c8c98fc645143","target":"record","created_at":"2026-05-18T03:37:09Z","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":"903022b2651f562ecc4fd2357eb97ed4c9602bf425f0645fef18d18b6ec7b6a3","cross_cats_sorted":[],"license":"","primary_cat":"math.CT","submitted_at":"2007-11-23T00:55:11Z","title_canon_sha256":"14894cb6b75d23f160eabc9f06edc34597f9bc3485c47b81e7bf07e8f90977a0"},"schema_version":"1.0","source":{"id":"0711.3659","kind":"arxiv","version":1}},"canonical_sha256":"a52fabaa08f56412c71a9646ae8251eac4330e6476886a2cdda39af0260e663f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a52fabaa08f56412c71a9646ae8251eac4330e6476886a2cdda39af0260e663f","first_computed_at":"2026-05-18T03:37:09.647567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:09.647567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vW6p9X8ErxmTPct5yL7Urjc2xl6sIczvbQXxwa3HNJoL0lb8SblvJgM1BQfR/VnP9beAUZXEWvku/HVqDtHeBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:09.648302Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.3659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cf8bff82105a31aa9289d3b08cf3837447669c066344e75431c8c98fc645143","sha256:e0a629449022b970dd43ba0814480f6cdd90c644a7e725886a104f02dd5e51ba"],"state_sha256":"6537a74a05f4d07cf1cb7535141b833e69ce2e2b62b2af9127466691668739b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lSo85iiTSGGhP9uOS/sqcEqA100CB6nFWKHgddMSnPjmrJPy+Q1QsOgMv0xIqPLTk/vQ15U9ngERnAQ3Ht6ZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:32:22.192782Z","bundle_sha256":"52d3674142bf61f4da261737b9f1bfc68f31f64d945f9a441d1c989fe6f1a7f0"}}