{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JPVEVIN7RFOPCO62BFNTN36HAS","short_pith_number":"pith:JPVEVIN7","canonical_record":{"source":{"id":"1307.0977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-03T11:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"2e3585771c9477b13f4292b1bc166881331808385a3eb3cfc3fbdc27f6825f8f","abstract_canon_sha256":"cd11035bb02624136b6fac5a9a1818080787c673e7bd32b6ec3034eeb244f5c5"},"schema_version":"1.0"},"canonical_sha256":"4bea4aa1bf895cf13bda095b36efc704aaefe56a767f983e7dc6f10f05a4cc8f","source":{"kind":"arxiv","id":"1307.0977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0977","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0977v1","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0977","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"JPVEVIN7RFOP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPVEVIN7RFOPCO62","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPVEVIN7","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JPVEVIN7RFOPCO62BFNTN36HAS","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-03T11:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"2e3585771c9477b13f4292b1bc166881331808385a3eb3cfc3fbdc27f6825f8f","abstract_canon_sha256":"cd11035bb02624136b6fac5a9a1818080787c673e7bd32b6ec3034eeb244f5c5"},"schema_version":"1.0"},"canonical_sha256":"4bea4aa1bf895cf13bda095b36efc704aaefe56a767f983e7dc6f10f05a4cc8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:23.561743Z","signature_b64":"4NJ2b70sLDhUunTnkbCF6/pQeNwcoIrcjhN8OqoG2PXN/1emOtTQjamCag2/TejjOBSre2aTXdjlbCMYscFxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bea4aa1bf895cf13bda095b36efc704aaefe56a767f983e7dc6f10f05a4cc8f","last_reissued_at":"2026-05-18T03:19:23.561183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:23.561183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0977","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":"2026-05-18T03:19:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kl5aW6joqhsz3d88mWZghzb+uwhC76BLUWjQHkNYw3GL/oB4fGhwp//X6kTLAmgvKU4a0jnyGsfQp4nUGrSiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:05:39.649743Z"},"content_sha256":"4030416a8d9ed108005672ddd8880b3e9bc5734174904f4b2228e927b5975d2d","schema_version":"1.0","event_id":"sha256:4030416a8d9ed108005672ddd8880b3e9bc5734174904f4b2228e927b5975d2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JPVEVIN7RFOPCO62BFNTN36HAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homology for one-dimensional solenoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ian F. Putnam, Massoud Amini, Sarah Saeidi Gholikandi","submitted_at":"2013-07-03T11:56:26Z","abstract_excerpt":"Smale space is a particular class of hyperbolic topological dynamical systems, defined by David Ruelle. The third author constructed a homology theory for Smale spaces which is based on Krieger's dimension group invariant for shifts of finite type. In this paper, we compute this homology for the one-dimensional generalized solenoids of R.F. Williams."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0977","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":""},"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":"2026-05-18T03:19:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GpW/kKEgsEQorpC3guuLzTVABxzHXisskXsM+YZj9r6M9nljbTynz2tpMeOGIbziM+0TQHz5y5knRR1mRkkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:05:39.650106Z"},"content_sha256":"bf97e62b2e5af609cdc86947ff82291f6ceea523aa0dab5908aaa19dd6abfa8b","schema_version":"1.0","event_id":"sha256:bf97e62b2e5af609cdc86947ff82291f6ceea523aa0dab5908aaa19dd6abfa8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPVEVIN7RFOPCO62BFNTN36HAS/bundle.json","state_url":"https://pith.science/pith/JPVEVIN7RFOPCO62BFNTN36HAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPVEVIN7RFOPCO62BFNTN36HAS/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":"2026-05-26T05:05:39Z","links":{"resolver":"https://pith.science/pith/JPVEVIN7RFOPCO62BFNTN36HAS","bundle":"https://pith.science/pith/JPVEVIN7RFOPCO62BFNTN36HAS/bundle.json","state":"https://pith.science/pith/JPVEVIN7RFOPCO62BFNTN36HAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPVEVIN7RFOPCO62BFNTN36HAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JPVEVIN7RFOPCO62BFNTN36HAS","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":"cd11035bb02624136b6fac5a9a1818080787c673e7bd32b6ec3034eeb244f5c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-03T11:56:26Z","title_canon_sha256":"2e3585771c9477b13f4292b1bc166881331808385a3eb3cfc3fbdc27f6825f8f"},"schema_version":"1.0","source":{"id":"1307.0977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0977","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0977v1","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0977","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"JPVEVIN7RFOP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPVEVIN7RFOPCO62","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPVEVIN7","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:bf97e62b2e5af609cdc86947ff82291f6ceea523aa0dab5908aaa19dd6abfa8b","target":"graph","created_at":"2026-05-18T03:19:23Z","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":"Smale space is a particular class of hyperbolic topological dynamical systems, defined by David Ruelle. The third author constructed a homology theory for Smale spaces which is based on Krieger's dimension group invariant for shifts of finite type. In this paper, we compute this homology for the one-dimensional generalized solenoids of R.F. Williams.","authors_text":"Ian F. Putnam, Massoud Amini, Sarah Saeidi Gholikandi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-03T11:56:26Z","title":"Homology for one-dimensional solenoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0977","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":"sha256:4030416a8d9ed108005672ddd8880b3e9bc5734174904f4b2228e927b5975d2d","target":"record","created_at":"2026-05-18T03:19:23Z","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":"cd11035bb02624136b6fac5a9a1818080787c673e7bd32b6ec3034eeb244f5c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-03T11:56:26Z","title_canon_sha256":"2e3585771c9477b13f4292b1bc166881331808385a3eb3cfc3fbdc27f6825f8f"},"schema_version":"1.0","source":{"id":"1307.0977","kind":"arxiv","version":1}},"canonical_sha256":"4bea4aa1bf895cf13bda095b36efc704aaefe56a767f983e7dc6f10f05a4cc8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bea4aa1bf895cf13bda095b36efc704aaefe56a767f983e7dc6f10f05a4cc8f","first_computed_at":"2026-05-18T03:19:23.561183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:23.561183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4NJ2b70sLDhUunTnkbCF6/pQeNwcoIrcjhN8OqoG2PXN/1emOtTQjamCag2/TejjOBSre2aTXdjlbCMYscFxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:23.561743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4030416a8d9ed108005672ddd8880b3e9bc5734174904f4b2228e927b5975d2d","sha256:bf97e62b2e5af609cdc86947ff82291f6ceea523aa0dab5908aaa19dd6abfa8b"],"state_sha256":"85ec096bdbc52f6cb5dcedc56037fba1dcb20c8520a58dce62929205147a8159"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cL00csN0n7CLMHCSXzZPbrA5OOfFeBqhF5b51csEdGGL5p60J8ti3bZ5bCXzpYid/RHJSAqwLaQ47WWtNhVpAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:05:39.652457Z","bundle_sha256":"1ed1c5b6b4703d22971c3b80c60f7be0ab955180dd3e311ba74b0095d31fdbec"}}