{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JIIMZTHT6DOQYN6NHPXCBABMQC","short_pith_number":"pith:JIIMZTHT","canonical_record":{"source":{"id":"1212.0157","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-01T20:42:03Z","cross_cats_sorted":[],"title_canon_sha256":"ab6fa733ea184875265226dfd97d323c2f2a6973ad9986b0a93f0069251cd6ea","abstract_canon_sha256":"bbde23ebc79d40452a5923a016d81494de72f5da3fa26e5ab82896ec0d9a4dc1"},"schema_version":"1.0"},"canonical_sha256":"4a10ccccf3f0dd0c37cd3bee20802c80a9d579d95f09d9b80cd05cd14afe2964","source":{"kind":"arxiv","id":"1212.0157","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0157","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0157v5","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0157","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"JIIMZTHT6DOQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JIIMZTHT6DOQYN6N","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JIIMZTHT","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JIIMZTHT6DOQYN6NHPXCBABMQC","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0157","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-01T20:42:03Z","cross_cats_sorted":[],"title_canon_sha256":"ab6fa733ea184875265226dfd97d323c2f2a6973ad9986b0a93f0069251cd6ea","abstract_canon_sha256":"bbde23ebc79d40452a5923a016d81494de72f5da3fa26e5ab82896ec0d9a4dc1"},"schema_version":"1.0"},"canonical_sha256":"4a10ccccf3f0dd0c37cd3bee20802c80a9d579d95f09d9b80cd05cd14afe2964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:40.924786Z","signature_b64":"SGeRqsN/qfFPzNBd5UODTTlo4rgSXmwSefLoD5YboLAgdHhsYCDrt5whfBF/KIHzQrwNiW5xaXa8OJfgPzg6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a10ccccf3f0dd0c37cd3bee20802c80a9d579d95f09d9b80cd05cd14afe2964","last_reissued_at":"2026-05-18T01:21:40.924258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:40.924258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0157","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YH2K29jfkBUvhAN/SDD7lGAutJQz1tewiY6cYl1M+DEtPXnNbd76d3kDsHO344lZy2p81ClFWc81hGZGcZ4ZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:52:26.052803Z"},"content_sha256":"b01e24eb02951221faedf14ae2e3a1b4c4416d61127ce6b8e5e200d8cfd220e7","schema_version":"1.0","event_id":"sha256:b01e24eb02951221faedf14ae2e3a1b4c4416d61127ce6b8e5e200d8cfd220e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JIIMZTHT6DOQYN6NHPXCBABMQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On uniform relationships between combinatorial problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damir D. Dzhafarov, Fran\\c{c}ois G. Dorais, Jeffry L. Hirst, Joseph R. Mileti, Paul Shafer","submitted_at":"2012-12-01T20:42:03Z","abstract_excerpt":"The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic. In this setting, called reverse mathematics, one investigates which theorems provably imply which others in a weak formal theory roughly corresponding to computable mathematics. Since the proofs of such implications take place in classical logic, they may in principle involve appeals to multiple applications of a particular theorem, or to non-uniform decisions about how to proceed in a given construction. In practice, however, if a theorem $\\mathsf{Q}$ implies a theore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0157","kind":"arxiv","version":5},"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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MH9kic/wAm8VoYYuHdmohgg2dozNTMMb4cLisoIdghpSfpXhlzES7m0jvXoZpMqoHiymI1hyhdIG35IOzyYmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:52:26.053459Z"},"content_sha256":"2164359870b9fb069d46fdcca29f4b5e381f76fb544f0ad72b76e05dfb1f7772","schema_version":"1.0","event_id":"sha256:2164359870b9fb069d46fdcca29f4b5e381f76fb544f0ad72b76e05dfb1f7772"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIIMZTHT6DOQYN6NHPXCBABMQC/bundle.json","state_url":"https://pith.science/pith/JIIMZTHT6DOQYN6NHPXCBABMQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIIMZTHT6DOQYN6NHPXCBABMQC/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":"2026-05-25T08:52:26Z","links":{"resolver":"https://pith.science/pith/JIIMZTHT6DOQYN6NHPXCBABMQC","bundle":"https://pith.science/pith/JIIMZTHT6DOQYN6NHPXCBABMQC/bundle.json","state":"https://pith.science/pith/JIIMZTHT6DOQYN6NHPXCBABMQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIIMZTHT6DOQYN6NHPXCBABMQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JIIMZTHT6DOQYN6NHPXCBABMQC","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":"bbde23ebc79d40452a5923a016d81494de72f5da3fa26e5ab82896ec0d9a4dc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-01T20:42:03Z","title_canon_sha256":"ab6fa733ea184875265226dfd97d323c2f2a6973ad9986b0a93f0069251cd6ea"},"schema_version":"1.0","source":{"id":"1212.0157","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0157","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0157v5","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0157","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"JIIMZTHT6DOQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JIIMZTHT6DOQYN6N","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JIIMZTHT","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:2164359870b9fb069d46fdcca29f4b5e381f76fb544f0ad72b76e05dfb1f7772","target":"graph","created_at":"2026-05-18T01:21:40Z","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":"The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic. In this setting, called reverse mathematics, one investigates which theorems provably imply which others in a weak formal theory roughly corresponding to computable mathematics. Since the proofs of such implications take place in classical logic, they may in principle involve appeals to multiple applications of a particular theorem, or to non-uniform decisions about how to proceed in a given construction. In practice, however, if a theorem $\\mathsf{Q}$ implies a theore","authors_text":"Damir D. Dzhafarov, Fran\\c{c}ois G. Dorais, Jeffry L. Hirst, Joseph R. Mileti, Paul Shafer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-01T20:42:03Z","title":"On uniform relationships between combinatorial problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0157","kind":"arxiv","version":5},"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:b01e24eb02951221faedf14ae2e3a1b4c4416d61127ce6b8e5e200d8cfd220e7","target":"record","created_at":"2026-05-18T01:21:40Z","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":"bbde23ebc79d40452a5923a016d81494de72f5da3fa26e5ab82896ec0d9a4dc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-12-01T20:42:03Z","title_canon_sha256":"ab6fa733ea184875265226dfd97d323c2f2a6973ad9986b0a93f0069251cd6ea"},"schema_version":"1.0","source":{"id":"1212.0157","kind":"arxiv","version":5}},"canonical_sha256":"4a10ccccf3f0dd0c37cd3bee20802c80a9d579d95f09d9b80cd05cd14afe2964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a10ccccf3f0dd0c37cd3bee20802c80a9d579d95f09d9b80cd05cd14afe2964","first_computed_at":"2026-05-18T01:21:40.924258Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:40.924258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGeRqsN/qfFPzNBd5UODTTlo4rgSXmwSefLoD5YboLAgdHhsYCDrt5whfBF/KIHzQrwNiW5xaXa8OJfgPzg6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:40.924786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0157","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b01e24eb02951221faedf14ae2e3a1b4c4416d61127ce6b8e5e200d8cfd220e7","sha256:2164359870b9fb069d46fdcca29f4b5e381f76fb544f0ad72b76e05dfb1f7772"],"state_sha256":"da990d2264d7d176d1c81d81692f4cf35423dd650a0d9cf6d948acca73de443f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NCw/9md9f8eZdZsPtxE0EbwscKiLXnVU6ao0BI9LNynZgVShBUb+uxZ7vAllt7iz/pBrBLpQgBeYgI+QzuACAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:52:26.056779Z","bundle_sha256":"ac1be6a1950a6d195c33762e8ce9e0c75b5f1221365c013f7d14ea9ec78b2dd3"}}