{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FHXOZORI7PTXHVRHZQ3S7TGUPG","short_pith_number":"pith:FHXOZORI","canonical_record":{"source":{"id":"1406.4786","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-18T16:43:29Z","cross_cats_sorted":[],"title_canon_sha256":"5e2d2dabe9a338b660f704816e5594a14b75b5513857edf5b54375dc6d6e8ba8","abstract_canon_sha256":"01df481c65d6433880b4769cb77e221a15e7caa23c9c600cb68ccbc1456dca90"},"schema_version":"1.0"},"canonical_sha256":"29eeecba28fbe773d627cc372fccd47991990afe30432e9b3040f46cf4f05d2f","source":{"kind":"arxiv","id":"1406.4786","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4786","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4786v3","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4786","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"FHXOZORI7PTX","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHXOZORI7PTXHVRH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHXOZORI","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FHXOZORI7PTXHVRHZQ3S7TGUPG","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4786","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-18T16:43:29Z","cross_cats_sorted":[],"title_canon_sha256":"5e2d2dabe9a338b660f704816e5594a14b75b5513857edf5b54375dc6d6e8ba8","abstract_canon_sha256":"01df481c65d6433880b4769cb77e221a15e7caa23c9c600cb68ccbc1456dca90"},"schema_version":"1.0"},"canonical_sha256":"29eeecba28fbe773d627cc372fccd47991990afe30432e9b3040f46cf4f05d2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:45.698484Z","signature_b64":"PrzE+eEww3Jg2I2/N6MIwgnbCqbJFUJxXz72od2UYQV1+jWineWWz7Ekf0GYyFHG8GkdksFge6Zdx0DYW3pvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29eeecba28fbe773d627cc372fccd47991990afe30432e9b3040f46cf4f05d2f","last_reissued_at":"2026-05-18T01:34:45.697878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:45.697878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4786","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":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Giyhp4y6qFHwjsj6KD0R2cBI7g8HjCHp2olv6NAg9qvKBLBbtN84+Mlj2bBkFnv94SPdEzWkJCl/Nlofr+6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:11:49.732069Z"},"content_sha256":"bd94fd8b7df5e80fd6ba3515406177b14018a71dd1fa0f92be9db816ab74956d","schema_version":"1.0","event_id":"sha256:bd94fd8b7df5e80fd6ba3515406177b14018a71dd1fa0f92be9db816ab74956d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FHXOZORI7PTXHVRHZQ3S7TGUPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of a connected component of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carl Mummert, Jeffry L. Hirst, Kirill Gura","submitted_at":"2014-06-18T16:43:29Z","abstract_excerpt":"We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to $\\mathsf{ACA}_0$ over $\\mathsf{RCA}_0$. The problem of decomposing a countable graph into connected components is strongly Weihrauch equivalent to the problem of finding a single component, and each is equivalent to its infinite parallelization. For graphs with finitely many connected components, the existence of a connected component is either provable in $\\mathsf{RCA}_0$ or is equivalent to induction"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4786","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":"2026-05-18T01:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r0vJf1dj7ZeS157/UZ9/szJp8lc9z+YyxszpjCXGcKbL5xZu8YUXKitaJhrct1fiIefpuihPenBsaKO/PhVxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:11:49.732429Z"},"content_sha256":"4c2b1356bd7e67622d3e25c31822a757357dd12359fd939a2d67d816192d3740","schema_version":"1.0","event_id":"sha256:4c2b1356bd7e67622d3e25c31822a757357dd12359fd939a2d67d816192d3740"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG/bundle.json","state_url":"https://pith.science/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG/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":"2026-05-28T03:11:49Z","links":{"resolver":"https://pith.science/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG","bundle":"https://pith.science/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG/bundle.json","state":"https://pith.science/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHXOZORI7PTXHVRHZQ3S7TGUPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FHXOZORI7PTXHVRHZQ3S7TGUPG","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":"01df481c65d6433880b4769cb77e221a15e7caa23c9c600cb68ccbc1456dca90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-18T16:43:29Z","title_canon_sha256":"5e2d2dabe9a338b660f704816e5594a14b75b5513857edf5b54375dc6d6e8ba8"},"schema_version":"1.0","source":{"id":"1406.4786","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4786","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4786v3","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4786","created_at":"2026-05-18T01:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"FHXOZORI7PTX","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHXOZORI7PTXHVRH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHXOZORI","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:4c2b1356bd7e67622d3e25c31822a757357dd12359fd939a2d67d816192d3740","target":"graph","created_at":"2026-05-18T01:34:45Z","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 study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to $\\mathsf{ACA}_0$ over $\\mathsf{RCA}_0$. The problem of decomposing a countable graph into connected components is strongly Weihrauch equivalent to the problem of finding a single component, and each is equivalent to its infinite parallelization. For graphs with finitely many connected components, the existence of a connected component is either provable in $\\mathsf{RCA}_0$ or is equivalent to induction","authors_text":"Carl Mummert, Jeffry L. Hirst, Kirill Gura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-18T16:43:29Z","title":"On the existence of a connected component of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4786","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:bd94fd8b7df5e80fd6ba3515406177b14018a71dd1fa0f92be9db816ab74956d","target":"record","created_at":"2026-05-18T01:34:45Z","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":"01df481c65d6433880b4769cb77e221a15e7caa23c9c600cb68ccbc1456dca90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-18T16:43:29Z","title_canon_sha256":"5e2d2dabe9a338b660f704816e5594a14b75b5513857edf5b54375dc6d6e8ba8"},"schema_version":"1.0","source":{"id":"1406.4786","kind":"arxiv","version":3}},"canonical_sha256":"29eeecba28fbe773d627cc372fccd47991990afe30432e9b3040f46cf4f05d2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29eeecba28fbe773d627cc372fccd47991990afe30432e9b3040f46cf4f05d2f","first_computed_at":"2026-05-18T01:34:45.697878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:45.697878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PrzE+eEww3Jg2I2/N6MIwgnbCqbJFUJxXz72od2UYQV1+jWineWWz7Ekf0GYyFHG8GkdksFge6Zdx0DYW3pvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:45.698484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4786","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd94fd8b7df5e80fd6ba3515406177b14018a71dd1fa0f92be9db816ab74956d","sha256:4c2b1356bd7e67622d3e25c31822a757357dd12359fd939a2d67d816192d3740"],"state_sha256":"348c0b862b051be96a8c9240e6ea3a143457c106c6ca52dae9c7eecda49451b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vUW+mokYZuixhGt4sPvI6qOjIdjVz69iMH5Y9Vj5FQ//otLgFLByGW5hDKgZPiHIyIYe0ogK7SjhpKqyRakDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:11:49.734407Z","bundle_sha256":"9668e822e2fe21f1051f5390b33ddde8f5848f0d10b7e9b764ae0e33d351b63d"}}