{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QWZFJKUU5A4YNIWLWRGX3LJD2X","short_pith_number":"pith:QWZFJKUU","canonical_record":{"source":{"id":"1305.6192","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T12:25:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7fb74661f67b96d45aaeffb04aab2404ac55042f343638e81072a0d77adad694","abstract_canon_sha256":"41e3e860473234b7dc5ab5d96180bcaf7ae040346c4a1d4a0a761830e96c4e86"},"schema_version":"1.0"},"canonical_sha256":"85b254aa94e83986a2cbb44d7dad23d5f8d8c504bbf5d5733066940ebc3bfb29","source":{"kind":"arxiv","id":"1305.6192","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6192","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6192v2","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6192","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"QWZFJKUU5A4Y","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QWZFJKUU5A4YNIWL","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QWZFJKUU","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QWZFJKUU5A4YNIWLWRGX3LJD2X","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6192","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T12:25:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7fb74661f67b96d45aaeffb04aab2404ac55042f343638e81072a0d77adad694","abstract_canon_sha256":"41e3e860473234b7dc5ab5d96180bcaf7ae040346c4a1d4a0a761830e96c4e86"},"schema_version":"1.0"},"canonical_sha256":"85b254aa94e83986a2cbb44d7dad23d5f8d8c504bbf5d5733066940ebc3bfb29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:24.252465Z","signature_b64":"tPoWm0Yrtz5jj2u9Ph43TLUdHvyOnO2fN8Grv6u/jJfDqkOzZKY8Uxk4zUPeCaVO/GGVNeS5/hWNVPkxB2AvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85b254aa94e83986a2cbb44d7dad23d5f8d8c504bbf5d5733066940ebc3bfb29","last_reissued_at":"2026-05-18T03:17:24.252091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:24.252091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6192","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":"2026-05-18T03:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4hDS3XgoIuXi/EKJMfqk1bDPAZhAe3a0E2xmQjvGOaHIrxSetSnISvaKh0J8bGmZCrbe8GMF4lLPucNsus8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:14:03.115287Z"},"content_sha256":"ba918b87796a31c2c430bba311eeb027f4f77ec082501467a554268d734980c3","schema_version":"1.0","event_id":"sha256:ba918b87796a31c2c430bba311eeb027f4f77ec082501467a554268d734980c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QWZFJKUU5A4YNIWLWRGX3LJD2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The M-Principal Graph of a Commutative Ring","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"F. Heydari, M.J. Nikmehr","submitted_at":"2013-05-27T12:25:33Z","abstract_excerpt":"This paper has been withdrawn by the author because there are some typos in proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6192","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":"2026-05-18T03:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YETW1lzjolT9DDx94/mOyYaxt9XixkyXnEJT+9N0/+4ca8f+vgu3ktKDu/IACrMNfNp5tbm6madLVpTez2brAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T06:14:03.115650Z"},"content_sha256":"87c51ac38ce914410e2ad630868dc7880817a27130e890d1d8cbb34125ebfedf","schema_version":"1.0","event_id":"sha256:87c51ac38ce914410e2ad630868dc7880817a27130e890d1d8cbb34125ebfedf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X/bundle.json","state_url":"https://pith.science/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X/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":"2026-06-26T06:14:03Z","links":{"resolver":"https://pith.science/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X","bundle":"https://pith.science/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X/bundle.json","state":"https://pith.science/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWZFJKUU5A4YNIWLWRGX3LJD2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QWZFJKUU5A4YNIWLWRGX3LJD2X","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":"41e3e860473234b7dc5ab5d96180bcaf7ae040346c4a1d4a0a761830e96c4e86","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T12:25:33Z","title_canon_sha256":"7fb74661f67b96d45aaeffb04aab2404ac55042f343638e81072a0d77adad694"},"schema_version":"1.0","source":{"id":"1305.6192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6192","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6192v2","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6192","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"QWZFJKUU5A4Y","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QWZFJKUU5A4YNIWL","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QWZFJKUU","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:87c51ac38ce914410e2ad630868dc7880817a27130e890d1d8cbb34125ebfedf","target":"graph","created_at":"2026-05-18T03:17:24Z","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":"This paper has been withdrawn by the author because there are some typos in proofs.","authors_text":"F. Heydari, M.J. Nikmehr","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T12:25:33Z","title":"The M-Principal Graph of a Commutative Ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6192","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:ba918b87796a31c2c430bba311eeb027f4f77ec082501467a554268d734980c3","target":"record","created_at":"2026-05-18T03:17:24Z","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":"41e3e860473234b7dc5ab5d96180bcaf7ae040346c4a1d4a0a761830e96c4e86","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T12:25:33Z","title_canon_sha256":"7fb74661f67b96d45aaeffb04aab2404ac55042f343638e81072a0d77adad694"},"schema_version":"1.0","source":{"id":"1305.6192","kind":"arxiv","version":2}},"canonical_sha256":"85b254aa94e83986a2cbb44d7dad23d5f8d8c504bbf5d5733066940ebc3bfb29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85b254aa94e83986a2cbb44d7dad23d5f8d8c504bbf5d5733066940ebc3bfb29","first_computed_at":"2026-05-18T03:17:24.252091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:24.252091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tPoWm0Yrtz5jj2u9Ph43TLUdHvyOnO2fN8Grv6u/jJfDqkOzZKY8Uxk4zUPeCaVO/GGVNeS5/hWNVPkxB2AvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:24.252465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba918b87796a31c2c430bba311eeb027f4f77ec082501467a554268d734980c3","sha256:87c51ac38ce914410e2ad630868dc7880817a27130e890d1d8cbb34125ebfedf"],"state_sha256":"222f6d687af1443ad3f837479870add5de5278dd6a4a9c6b70614341807445a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OetasI+GXy/iAHWIu3xt4DsqhpmQ8xwhxJi9daCssAN5KH5gALvWv6f9f8FzXVP38yVJxNaBpX0T12OJIVZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T06:14:03.118929Z","bundle_sha256":"614ceeb401c45c40b9e65d5bc81ed988bc13ae6a0c30a666b576f719d92aa033"}}