{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6QBQMR7APJU5FVXIDQJWRK3VQZ","short_pith_number":"pith:6QBQMR7A","canonical_record":{"source":{"id":"1110.1848","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-09T15:05:23Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2de136b089f0f6809be48e35b5d276441c49c1d981d4dd56fe16bb7ba397c162","abstract_canon_sha256":"e99e4f16df55095a1853129b12d4ba40b9ae2d6db722e5b29a1ea1756690254f"},"schema_version":"1.0"},"canonical_sha256":"f4030647e07a69d2d6e81c1368ab75864c17c5d54ca2cd9ae77e7269b80e60be","source":{"kind":"arxiv","id":"1110.1848","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1848","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1848v2","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1848","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"6QBQMR7APJU5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6QBQMR7APJU5FVXI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6QBQMR7A","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6QBQMR7APJU5FVXIDQJWRK3VQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1848","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-09T15:05:23Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"2de136b089f0f6809be48e35b5d276441c49c1d981d4dd56fe16bb7ba397c162","abstract_canon_sha256":"e99e4f16df55095a1853129b12d4ba40b9ae2d6db722e5b29a1ea1756690254f"},"schema_version":"1.0"},"canonical_sha256":"f4030647e07a69d2d6e81c1368ab75864c17c5d54ca2cd9ae77e7269b80e60be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:57.174810Z","signature_b64":"tjmlvAeVvqBMY8a3GkF2aHSlIbVUKfEaAAHSVnMiQinrN5VhFCiQsY/Qcss98WHCZv3QE+uJO5pQWX3QhLJACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4030647e07a69d2d6e81c1368ab75864c17c5d54ca2cd9ae77e7269b80e60be","last_reissued_at":"2026-05-17T23:41:57.174319Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:57.174319Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1848","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":"2026-05-17T23:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMaoPa6UG9/S5SylLPAaQlTuGGJ3TR0d/OQy7i2PAZMovthV6Zu7SRyNkpvE8g1LHhdUbBAvXM1kcTGL0iJDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:35:40.321360Z"},"content_sha256":"aa369f47aff7853d75b6ea8d5c2206bd9bf5e0c0d009d403e14768e5b90c17a6","schema_version":"1.0","event_id":"sha256:aa369f47aff7853d75b6ea8d5c2206bd9bf5e0c0d009d403e14768e5b90c17a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6QBQMR7APJU5FVXIDQJWRK3VQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Saeed Salehi","submitted_at":"2011-10-09T15:05:23Z","abstract_excerpt":"We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of ${\\rm I\\Delta_0}$ whose Herbrand Consistency is not provable in the thoery ${\\rm I\\Delta_0}$. We also show the existence of an ${\\rm I\\Delta_0}-$derivable $\\Pi_1-$sentence such that ${\\rm I\\Delta_0}$ cannot prove its Herbrand Consistency."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1848","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":"2026-05-17T23:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAW6riknOw7CoSG9ATpQMjFVBr0SlmuUqDPvjFccE+1jPZmlKvyctqNZ/jPof4J/dTeI/12T+A1OVd/b2UonCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:35:40.321715Z"},"content_sha256":"060304b34058b3aab0942f0d722af96742165c481e017f25927919190ce31c69","schema_version":"1.0","event_id":"sha256:060304b34058b3aab0942f0d722af96742165c481e017f25927919190ce31c69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ/bundle.json","state_url":"https://pith.science/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ/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":"2026-06-26T11:35:40Z","links":{"resolver":"https://pith.science/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ","bundle":"https://pith.science/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ/bundle.json","state":"https://pith.science/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QBQMR7APJU5FVXIDQJWRK3VQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6QBQMR7APJU5FVXIDQJWRK3VQZ","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":"e99e4f16df55095a1853129b12d4ba40b9ae2d6db722e5b29a1ea1756690254f","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-09T15:05:23Z","title_canon_sha256":"2de136b089f0f6809be48e35b5d276441c49c1d981d4dd56fe16bb7ba397c162"},"schema_version":"1.0","source":{"id":"1110.1848","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1848","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1848v2","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1848","created_at":"2026-05-17T23:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"6QBQMR7APJU5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6QBQMR7APJU5FVXI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6QBQMR7A","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:060304b34058b3aab0942f0d722af96742165c481e017f25927919190ce31c69","target":"graph","created_at":"2026-05-17T23:41:57Z","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 formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of ${\\rm I\\Delta_0}$ whose Herbrand Consistency is not provable in the thoery ${\\rm I\\Delta_0}$. We also show the existence of an ${\\rm I\\Delta_0}-$derivable $\\Pi_1-$sentence such that ${\\rm I\\Delta_0}$ cannot prove its Herbrand Consistency.","authors_text":"Saeed Salehi","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-09T15:05:23Z","title":"Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1848","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:aa369f47aff7853d75b6ea8d5c2206bd9bf5e0c0d009d403e14768e5b90c17a6","target":"record","created_at":"2026-05-17T23:41:57Z","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":"e99e4f16df55095a1853129b12d4ba40b9ae2d6db722e5b29a1ea1756690254f","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-10-09T15:05:23Z","title_canon_sha256":"2de136b089f0f6809be48e35b5d276441c49c1d981d4dd56fe16bb7ba397c162"},"schema_version":"1.0","source":{"id":"1110.1848","kind":"arxiv","version":2}},"canonical_sha256":"f4030647e07a69d2d6e81c1368ab75864c17c5d54ca2cd9ae77e7269b80e60be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4030647e07a69d2d6e81c1368ab75864c17c5d54ca2cd9ae77e7269b80e60be","first_computed_at":"2026-05-17T23:41:57.174319Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:57.174319Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tjmlvAeVvqBMY8a3GkF2aHSlIbVUKfEaAAHSVnMiQinrN5VhFCiQsY/Qcss98WHCZv3QE+uJO5pQWX3QhLJACA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:57.174810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1848","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa369f47aff7853d75b6ea8d5c2206bd9bf5e0c0d009d403e14768e5b90c17a6","sha256:060304b34058b3aab0942f0d722af96742165c481e017f25927919190ce31c69"],"state_sha256":"c36f97e8d3b20d87a2dfc814eb634ea4f0a76927c250e20a8277e396098d4b98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKOF/47qlXzK/J1hRlJ2mAkRnKmKJk91bqcLaieNPJnxetqfthVMnisF3x0NEevWJ4SKr1qFOVbvWYSUZNknCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:35:40.323646Z","bundle_sha256":"463654d83216934cb97d7dfc0b3ea6a291c54880b9531b8dcf036b66611918a3"}}