{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:W3XIISI7ZNRFCJSZ2CLK6U52FG","short_pith_number":"pith:W3XIISI7","canonical_record":{"source":{"id":"0708.0947","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2007-08-07T14:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"50b9f44ef2ffe4e45957adf858cc94b80971201a14a1389fe0d6626a86ed3a2a","abstract_canon_sha256":"5d2bab601df89e008d358f2bc259f9938f4576b0d4b6b7ef662e75e28571ae99"},"schema_version":"1.0"},"canonical_sha256":"b6ee84491fcb62512659d096af53ba298cf7d605c0d0abe6d9cd7a5483600bf6","source":{"kind":"arxiv","id":"0708.0947","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0947","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0947v1","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0947","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"W3XIISI7ZNRF","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"pith_short_16","alias_value":"W3XIISI7ZNRFCJSZ","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"pith_short_8","alias_value":"W3XIISI7","created_at":"2026-07-04T15:03:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:W3XIISI7ZNRFCJSZ2CLK6U52FG","target":"record","payload":{"canonical_record":{"source":{"id":"0708.0947","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2007-08-07T14:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"50b9f44ef2ffe4e45957adf858cc94b80971201a14a1389fe0d6626a86ed3a2a","abstract_canon_sha256":"5d2bab601df89e008d358f2bc259f9938f4576b0d4b6b7ef662e75e28571ae99"},"schema_version":"1.0"},"canonical_sha256":"b6ee84491fcb62512659d096af53ba298cf7d605c0d0abe6d9cd7a5483600bf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:03:30.748838Z","signature_b64":"ectvby2tXi478vyhjZAFMPmGyq3x96KlPdpImmV9xz3C2me74EJRywdDfAWnC/GOsfHagff+2EzBk/HN4aTQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6ee84491fcb62512659d096af53ba298cf7d605c0d0abe6d9cd7a5483600bf6","last_reissued_at":"2026-07-04T15:03:30.748432Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:03:30.748432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.0947","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":"2026-07-04T15:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohRcN3wDWCKYsu4+Y352y9MZPMeKGQrNSueLrY0SLr8/TqNwGEQezIPLGH8u6VXJnWuV8GzFWWbTcltspENRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:00:32.475300Z"},"content_sha256":"970b5c5fa0a3e656058cc6784b9e198f1cd8dd58447eb23f071b9a63b09c5e85","schema_version":"1.0","event_id":"sha256:970b5c5fa0a3e656058cc6784b9e198f1cd8dd58447eb23f071b9a63b09c5e85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:W3XIISI7ZNRFCJSZ2CLK6U52FG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational semigroup automata","license":"","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Elaine Render, Mark Kambites","submitted_at":"2007-08-07T14:26:48Z","abstract_excerpt":"We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such family arises as the family of languages accepted by N-automata where N is a simple or 0-simple monoid. A consequence is that every such family is either the class of regular languages, contains all the blind one-counter languages, or is the family of languages accepted by G-automata for G a non-locally-finite torsion group.\n  We consider a natural extensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0947","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/0708.0947/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":"2026-07-04T15:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tdoM7UozbpGq0rAEcECF8Kh2fvyKFCZoQZr6AS/HY77qzqawuJLQzd2Nb2yHJcoSqGmvylqaSBNxcIlCFXmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:00:32.475678Z"},"content_sha256":"5412943ae64d66cf75e0c9c2824b5f893d573cfb77f2919cb3916d5e5e5fe54c","schema_version":"1.0","event_id":"sha256:5412943ae64d66cf75e0c9c2824b5f893d573cfb77f2919cb3916d5e5e5fe54c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG/bundle.json","state_url":"https://pith.science/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG/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":"2026-07-05T07:00:32Z","links":{"resolver":"https://pith.science/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG","bundle":"https://pith.science/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG/bundle.json","state":"https://pith.science/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3XIISI7ZNRFCJSZ2CLK6U52FG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:W3XIISI7ZNRFCJSZ2CLK6U52FG","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":"5d2bab601df89e008d358f2bc259f9938f4576b0d4b6b7ef662e75e28571ae99","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2007-08-07T14:26:48Z","title_canon_sha256":"50b9f44ef2ffe4e45957adf858cc94b80971201a14a1389fe0d6626a86ed3a2a"},"schema_version":"1.0","source":{"id":"0708.0947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0947","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0947v1","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0947","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"W3XIISI7ZNRF","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"pith_short_16","alias_value":"W3XIISI7ZNRFCJSZ","created_at":"2026-07-04T15:03:30Z"},{"alias_kind":"pith_short_8","alias_value":"W3XIISI7","created_at":"2026-07-04T15:03:30Z"}],"graph_snapshots":[{"event_id":"sha256:5412943ae64d66cf75e0c9c2824b5f893d573cfb77f2919cb3916d5e5e5fe54c","target":"graph","created_at":"2026-07-04T15:03:30Z","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/0708.0947/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such family arises as the family of languages accepted by N-automata where N is a simple or 0-simple monoid. A consequence is that every such family is either the class of regular languages, contains all the blind one-counter languages, or is the family of languages accepted by G-automata for G a non-locally-finite torsion group.\n  We consider a natural extensio","authors_text":"Elaine Render, Mark Kambites","cross_cats":[],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2007-08-07T14:26:48Z","title":"Rational semigroup automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0947","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":"sha256:970b5c5fa0a3e656058cc6784b9e198f1cd8dd58447eb23f071b9a63b09c5e85","target":"record","created_at":"2026-07-04T15:03:30Z","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":"5d2bab601df89e008d358f2bc259f9938f4576b0d4b6b7ef662e75e28571ae99","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2007-08-07T14:26:48Z","title_canon_sha256":"50b9f44ef2ffe4e45957adf858cc94b80971201a14a1389fe0d6626a86ed3a2a"},"schema_version":"1.0","source":{"id":"0708.0947","kind":"arxiv","version":1}},"canonical_sha256":"b6ee84491fcb62512659d096af53ba298cf7d605c0d0abe6d9cd7a5483600bf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6ee84491fcb62512659d096af53ba298cf7d605c0d0abe6d9cd7a5483600bf6","first_computed_at":"2026-07-04T15:03:30.748432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:03:30.748432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ectvby2tXi478vyhjZAFMPmGyq3x96KlPdpImmV9xz3C2me74EJRywdDfAWnC/GOsfHagff+2EzBk/HN4aTQBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:03:30.748838Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.0947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:970b5c5fa0a3e656058cc6784b9e198f1cd8dd58447eb23f071b9a63b09c5e85","sha256:5412943ae64d66cf75e0c9c2824b5f893d573cfb77f2919cb3916d5e5e5fe54c"],"state_sha256":"cc41ca447d6ffaa0ba8f50e0ed9a931aa23b05032c0cf045927611737b0480ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ybz0nJk3jBrYF0IO2v924sCBh2JZRn0x91A2jrKuoaMJ0A1MohEagbOYJwdWon7mvuKN2S4DXFWKdHSt2pxgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T07:00:32.477539Z","bundle_sha256":"2bace05689b8ffccafbaa484e424be77f27ba14a7c08994242945eb31d054c62"}}