{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QI5ZM6POYKPBCXSLQKUJDUWCDS","short_pith_number":"pith:QI5ZM6PO","canonical_record":{"source":{"id":"1501.03690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-01-15T14:26:23Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9f710460415df92a8ff4fc6f91e4539b92636a25d3a8499afbd14abc1a095d9e","abstract_canon_sha256":"48135bc40b278ebdea31792e1be5023e2d8f62ca4f3bb15def3827cade25a0a6"},"schema_version":"1.0"},"canonical_sha256":"823b9679eec29e115e4b82a891d2c21ca524ee4b182e5ca1b6f8e443a1c4088b","source":{"kind":"arxiv","id":"1501.03690","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03690","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03690v3","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03690","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"QI5ZM6POYKPB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QI5ZM6POYKPBCXSL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QI5ZM6PO","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QI5ZM6POYKPBCXSLQKUJDUWCDS","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-01-15T14:26:23Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9f710460415df92a8ff4fc6f91e4539b92636a25d3a8499afbd14abc1a095d9e","abstract_canon_sha256":"48135bc40b278ebdea31792e1be5023e2d8f62ca4f3bb15def3827cade25a0a6"},"schema_version":"1.0"},"canonical_sha256":"823b9679eec29e115e4b82a891d2c21ca524ee4b182e5ca1b6f8e443a1c4088b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:07.171942Z","signature_b64":"QGrZDmZUadkRnjhz9f4IMOoN2rc8JcBe1q3ERbeNilPww4fBePBHVQJBf1mq+4b6SbwV6j9wOHa7NUNqoJSWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"823b9679eec29e115e4b82a891d2c21ca524ee4b182e5ca1b6f8e443a1c4088b","last_reissued_at":"2026-05-18T01:09:07.171499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:07.171499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03690","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkNIKJorHj73gX51kB180lH/eSodKfKKocia6Btcs8B6c2VgMZhnWEz8VedHVRy4MAi+8joMSA/BHFJhk7RLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:40:51.951505Z"},"content_sha256":"cf55eb07cffd99bf8af07b61a7c8ac4fbfdbcd6b88c003d83c7f2e81dead5bbe","schema_version":"1.0","event_id":"sha256:cf55eb07cffd99bf8af07b61a7c8ac4fbfdbcd6b88c003d83c7f2e81dead5bbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QI5ZM6POYKPBCXSLQKUJDUWCDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Double Inverse Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Darien DeWolf, Dorette Pronk","submitted_at":"2015-01-15T14:26:23Z","abstract_excerpt":"We show that the two binary operations in double inverse semigroups, as considered by Kock [2007], necessarily coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03690","kind":"arxiv","version":3},"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":"2026-05-18T01:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XvTRCqSDgPFluELMehYuzfUFf4Nqmcqx02v5l38g6OVR23nxWA/ve7v2ViFsRpgHpjqEcsvObJAcZwWY0mYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:40:51.951847Z"},"content_sha256":"c6e4e0b3ec2b9815fbee6eb32eaffab6c8b7df3d9737216e3e4dbcf86500baaf","schema_version":"1.0","event_id":"sha256:c6e4e0b3ec2b9815fbee6eb32eaffab6c8b7df3d9737216e3e4dbcf86500baaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS/bundle.json","state_url":"https://pith.science/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS/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":"2026-06-22T20:40:51Z","links":{"resolver":"https://pith.science/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS","bundle":"https://pith.science/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS/bundle.json","state":"https://pith.science/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QI5ZM6POYKPBCXSLQKUJDUWCDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QI5ZM6POYKPBCXSLQKUJDUWCDS","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":"48135bc40b278ebdea31792e1be5023e2d8f62ca4f3bb15def3827cade25a0a6","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-01-15T14:26:23Z","title_canon_sha256":"9f710460415df92a8ff4fc6f91e4539b92636a25d3a8499afbd14abc1a095d9e"},"schema_version":"1.0","source":{"id":"1501.03690","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03690","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03690v3","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03690","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"QI5ZM6POYKPB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QI5ZM6POYKPBCXSL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QI5ZM6PO","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:c6e4e0b3ec2b9815fbee6eb32eaffab6c8b7df3d9737216e3e4dbcf86500baaf","target":"graph","created_at":"2026-05-18T01:09:07Z","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":"We show that the two binary operations in double inverse semigroups, as considered by Kock [2007], necessarily coincide.","authors_text":"Darien DeWolf, Dorette Pronk","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-01-15T14:26:23Z","title":"On Double Inverse Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03690","kind":"arxiv","version":3},"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:cf55eb07cffd99bf8af07b61a7c8ac4fbfdbcd6b88c003d83c7f2e81dead5bbe","target":"record","created_at":"2026-05-18T01:09:07Z","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":"48135bc40b278ebdea31792e1be5023e2d8f62ca4f3bb15def3827cade25a0a6","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-01-15T14:26:23Z","title_canon_sha256":"9f710460415df92a8ff4fc6f91e4539b92636a25d3a8499afbd14abc1a095d9e"},"schema_version":"1.0","source":{"id":"1501.03690","kind":"arxiv","version":3}},"canonical_sha256":"823b9679eec29e115e4b82a891d2c21ca524ee4b182e5ca1b6f8e443a1c4088b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823b9679eec29e115e4b82a891d2c21ca524ee4b182e5ca1b6f8e443a1c4088b","first_computed_at":"2026-05-18T01:09:07.171499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:07.171499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QGrZDmZUadkRnjhz9f4IMOoN2rc8JcBe1q3ERbeNilPww4fBePBHVQJBf1mq+4b6SbwV6j9wOHa7NUNqoJSWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:07.171942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03690","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf55eb07cffd99bf8af07b61a7c8ac4fbfdbcd6b88c003d83c7f2e81dead5bbe","sha256:c6e4e0b3ec2b9815fbee6eb32eaffab6c8b7df3d9737216e3e4dbcf86500baaf"],"state_sha256":"65039c90c2312d0f80bbe8e5067b6b42cabd3c695690461c090464a757d08290"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CqzNqV/ot6RERg1VFLhMlbMfINzETBq4H21iiFw/oFQCPKmPrLk8VbuQILJBbpwHe3U/CJL5+9MgKmJrz9lsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:40:51.953790Z","bundle_sha256":"c807332161562baf8fbc2b798cb35c804b460ce9e033e527accd85b917705c1b"}}