{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6PTPUNPZKSRBCKEE2Y67THDTYG","short_pith_number":"pith:6PTPUNPZ","canonical_record":{"source":{"id":"1104.5646","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-04-29T15:02:12Z","cross_cats_sorted":["cs.CG","cs.DS"],"title_canon_sha256":"beafc70ebb82e7241d848a17e5f39db6088e8c121b13c0afe032368622b32d8c","abstract_canon_sha256":"d9235668826ee6d067b95ca542730769419f3d37b566a4f7bb1852cd3ffea45d"},"schema_version":"1.0"},"canonical_sha256":"f3e6fa35f954a2112884d63df99c73c197c2e05170d6e85985951ed84f14b733","source":{"kind":"arxiv","id":"1104.5646","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5646","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5646v5","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5646","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"6PTPUNPZKSRB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6PTPUNPZKSRBCKEE","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6PTPUNPZ","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6PTPUNPZKSRBCKEE2Y67THDTYG","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5646","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-04-29T15:02:12Z","cross_cats_sorted":["cs.CG","cs.DS"],"title_canon_sha256":"beafc70ebb82e7241d848a17e5f39db6088e8c121b13c0afe032368622b32d8c","abstract_canon_sha256":"d9235668826ee6d067b95ca542730769419f3d37b566a4f7bb1852cd3ffea45d"},"schema_version":"1.0"},"canonical_sha256":"f3e6fa35f954a2112884d63df99c73c197c2e05170d6e85985951ed84f14b733","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:00.758193Z","signature_b64":"j+h2zVzGgm7mn9lco3Srkt3985IdNByLXkq5FYVMfvRs/lSzfyKoRAZhXopYZARGRWMdc0e6VWuK1iupMjgsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3e6fa35f954a2112884d63df99c73c197c2e05170d6e85985951ed84f14b733","last_reissued_at":"2026-05-18T02:22:00.757406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:00.757406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5646","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":"2026-05-18T02:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DU35ox0dd47pEXNPIc3GJ/yVUvVXWRcjrn0s0LclwrJNzvF6jNE9HWuMQ/18U96dbxPqcqARHSR2VucVFZnDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:04:33.160366Z"},"content_sha256":"6dd7768b4b068451bfbeb1bc4fd26e36c21798c3246bc86690f64d0abf629ecc","schema_version":"1.0","event_id":"sha256:6dd7768b4b068451bfbeb1bc4fd26e36c21798c3246bc86690f64d0abf629ecc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6PTPUNPZKSRBCKEE2Y67THDTYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistence for Circle Valued Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DS"],"primary_cat":"math.AT","authors_text":"Dan Burghelea, Tamal K. Dey","submitted_at":"2011-04-29T15:02:12Z","abstract_excerpt":"We study circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the source space and its relevant subspaces. Unlike persistence of real valued maps, circle valued maps enjoy a different class of invariants called Jordan cells in addition to bar codes. We establish a relation between the homology of the source space and of its relevant subspaces with these invariants and provide a new algorithm to compute these invariants fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5646","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":"2026-05-18T02:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGG+j7c6yQfIRReBUJFlP+j4khhRi8vjh1hJ//vyA7Gp1PD+n1wNkJkKYfDy8f+myElM3cV2CFTZXeEVsci8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:04:33.160716Z"},"content_sha256":"efd03c2b939c99f0f460400600116f230591ef96f018d8524aab2f8d8ea6c9c6","schema_version":"1.0","event_id":"sha256:efd03c2b939c99f0f460400600116f230591ef96f018d8524aab2f8d8ea6c9c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PTPUNPZKSRBCKEE2Y67THDTYG/bundle.json","state_url":"https://pith.science/pith/6PTPUNPZKSRBCKEE2Y67THDTYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PTPUNPZKSRBCKEE2Y67THDTYG/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":"2026-06-25T08:04:33Z","links":{"resolver":"https://pith.science/pith/6PTPUNPZKSRBCKEE2Y67THDTYG","bundle":"https://pith.science/pith/6PTPUNPZKSRBCKEE2Y67THDTYG/bundle.json","state":"https://pith.science/pith/6PTPUNPZKSRBCKEE2Y67THDTYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PTPUNPZKSRBCKEE2Y67THDTYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6PTPUNPZKSRBCKEE2Y67THDTYG","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":"d9235668826ee6d067b95ca542730769419f3d37b566a4f7bb1852cd3ffea45d","cross_cats_sorted":["cs.CG","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-04-29T15:02:12Z","title_canon_sha256":"beafc70ebb82e7241d848a17e5f39db6088e8c121b13c0afe032368622b32d8c"},"schema_version":"1.0","source":{"id":"1104.5646","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5646","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5646v5","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5646","created_at":"2026-05-18T02:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"6PTPUNPZKSRB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6PTPUNPZKSRBCKEE","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6PTPUNPZ","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:efd03c2b939c99f0f460400600116f230591ef96f018d8524aab2f8d8ea6c9c6","target":"graph","created_at":"2026-05-18T02:22:00Z","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 circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the source space and its relevant subspaces. Unlike persistence of real valued maps, circle valued maps enjoy a different class of invariants called Jordan cells in addition to bar codes. We establish a relation between the homology of the source space and of its relevant subspaces with these invariants and provide a new algorithm to compute these invariants fr","authors_text":"Dan Burghelea, Tamal K. Dey","cross_cats":["cs.CG","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-04-29T15:02:12Z","title":"Persistence for Circle Valued Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5646","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":"sha256:6dd7768b4b068451bfbeb1bc4fd26e36c21798c3246bc86690f64d0abf629ecc","target":"record","created_at":"2026-05-18T02:22:00Z","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":"d9235668826ee6d067b95ca542730769419f3d37b566a4f7bb1852cd3ffea45d","cross_cats_sorted":["cs.CG","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-04-29T15:02:12Z","title_canon_sha256":"beafc70ebb82e7241d848a17e5f39db6088e8c121b13c0afe032368622b32d8c"},"schema_version":"1.0","source":{"id":"1104.5646","kind":"arxiv","version":5}},"canonical_sha256":"f3e6fa35f954a2112884d63df99c73c197c2e05170d6e85985951ed84f14b733","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3e6fa35f954a2112884d63df99c73c197c2e05170d6e85985951ed84f14b733","first_computed_at":"2026-05-18T02:22:00.757406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:00.757406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+h2zVzGgm7mn9lco3Srkt3985IdNByLXkq5FYVMfvRs/lSzfyKoRAZhXopYZARGRWMdc0e6VWuK1iupMjgsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:00.758193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5646","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dd7768b4b068451bfbeb1bc4fd26e36c21798c3246bc86690f64d0abf629ecc","sha256:efd03c2b939c99f0f460400600116f230591ef96f018d8524aab2f8d8ea6c9c6"],"state_sha256":"51ca88c694bae6c18e3de7f28c27dfdaf7b681e73d937ef5b6ebf1739930dd44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C27t8nENunFpr3kG9r5FmSAwuCo6lQgJ3X9CH/xE5n8MChzd8Q81oEI6m2Zvnxo/7uFypCPad2DZJlhWHgLnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:04:33.162785Z","bundle_sha256":"7b28979569b0bbc538ebca0a0b12ccb8574a0d376f109b8c8f5caf7f848ddf0e"}}