{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VIGQA2CK7UREGKFONEDRHCDF5L","short_pith_number":"pith:VIGQA2CK","canonical_record":{"source":{"id":"1306.1158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-05T15:54:19Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"a9507eaa887c3f9797e91e7b2ff63d440066cfd350ea931321b9b4320c153733","abstract_canon_sha256":"c23bd61b16bf4e4a0fd1e501dba38ae2aa488d6326ba79a3b7fc5f898879c5d6"},"schema_version":"1.0"},"canonical_sha256":"aa0d00684afd224328ae6907138865eade31f345829ebe5924d83742000c8608","source":{"kind":"arxiv","id":"1306.1158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1158","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1158v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1158","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"VIGQA2CK7URE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VIGQA2CK7UREGKFO","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VIGQA2CK","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VIGQA2CK7UREGKFONEDRHCDF5L","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-05T15:54:19Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"a9507eaa887c3f9797e91e7b2ff63d440066cfd350ea931321b9b4320c153733","abstract_canon_sha256":"c23bd61b16bf4e4a0fd1e501dba38ae2aa488d6326ba79a3b7fc5f898879c5d6"},"schema_version":"1.0"},"canonical_sha256":"aa0d00684afd224328ae6907138865eade31f345829ebe5924d83742000c8608","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:44.124236Z","signature_b64":"RwP/Tzbi3naA5+iyGW0ZjUysNEIa9S78cRSJDI5upciZqLydNWutTzbuIHlL1W0fYNxaSsAdcmt27akTnjJSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa0d00684afd224328ae6907138865eade31f345829ebe5924d83742000c8608","last_reissued_at":"2026-05-18T03:21:44.123448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:44.123448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1158","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":"2026-05-18T03:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DIwtvriXtSB3j+ELp/9UEJgSgsJw87DfJOeEjhtIpHTwau8keNIz89tggyUU+cnikcyDjxo5xuT/hWuKBdaXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:29:14.200635Z"},"content_sha256":"56a486efdce7b05419bdd856079764fc2dbcc9b88079d253cdd389b94d4b387e","schema_version":"1.0","event_id":"sha256:56a486efdce7b05419bdd856079764fc2dbcc9b88079d253cdd389b94d4b387e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VIGQA2CK7UREGKFONEDRHCDF5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed computation of homology using harmonics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"math.AT","authors_text":"Hamid Krim, Harish Chintakunta","submitted_at":"2013-06-05T15:54:19Z","abstract_excerpt":"We present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a basis for algebraic 1-cycles, and then use harmonics to efficiently identify the contractible and homologous cycles. The computational complexity of the algorithm is $O(|P|^\\omega)$, where $|P|$ is much smaller than the number of edges, and $\\omega$ is the complexity order of matrix multiplication. For geometric graphs, we show using simulations that $|P|$ is v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1158","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":"2026-05-18T03:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf4KmYXdfkZLukM2tVrRqMNoW9TVKwhEK9Ue2+kun0fUjIPJmiQTXSgjS8jx+1AF4HDVvfRXCTGSli2DORkBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:29:14.201297Z"},"content_sha256":"80cee5f4204d2283015034c0c003bcd43d3bcb3f4b59e8a7252a8883f339e132","schema_version":"1.0","event_id":"sha256:80cee5f4204d2283015034c0c003bcd43d3bcb3f4b59e8a7252a8883f339e132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VIGQA2CK7UREGKFONEDRHCDF5L/bundle.json","state_url":"https://pith.science/pith/VIGQA2CK7UREGKFONEDRHCDF5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VIGQA2CK7UREGKFONEDRHCDF5L/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":"2026-05-25T19:29:14Z","links":{"resolver":"https://pith.science/pith/VIGQA2CK7UREGKFONEDRHCDF5L","bundle":"https://pith.science/pith/VIGQA2CK7UREGKFONEDRHCDF5L/bundle.json","state":"https://pith.science/pith/VIGQA2CK7UREGKFONEDRHCDF5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VIGQA2CK7UREGKFONEDRHCDF5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VIGQA2CK7UREGKFONEDRHCDF5L","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":"c23bd61b16bf4e4a0fd1e501dba38ae2aa488d6326ba79a3b7fc5f898879c5d6","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-05T15:54:19Z","title_canon_sha256":"a9507eaa887c3f9797e91e7b2ff63d440066cfd350ea931321b9b4320c153733"},"schema_version":"1.0","source":{"id":"1306.1158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1158","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1158v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1158","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"VIGQA2CK7URE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VIGQA2CK7UREGKFO","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VIGQA2CK","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:80cee5f4204d2283015034c0c003bcd43d3bcb3f4b59e8a7252a8883f339e132","target":"graph","created_at":"2026-05-18T03:21:44Z","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 present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a basis for algebraic 1-cycles, and then use harmonics to efficiently identify the contractible and homologous cycles. The computational complexity of the algorithm is $O(|P|^\\omega)$, where $|P|$ is much smaller than the number of edges, and $\\omega$ is the complexity order of matrix multiplication. For geometric graphs, we show using simulations that $|P|$ is v","authors_text":"Hamid Krim, Harish Chintakunta","cross_cats":["cs.DC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-05T15:54:19Z","title":"Distributed computation of homology using harmonics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1158","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":"sha256:56a486efdce7b05419bdd856079764fc2dbcc9b88079d253cdd389b94d4b387e","target":"record","created_at":"2026-05-18T03:21:44Z","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":"c23bd61b16bf4e4a0fd1e501dba38ae2aa488d6326ba79a3b7fc5f898879c5d6","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-05T15:54:19Z","title_canon_sha256":"a9507eaa887c3f9797e91e7b2ff63d440066cfd350ea931321b9b4320c153733"},"schema_version":"1.0","source":{"id":"1306.1158","kind":"arxiv","version":1}},"canonical_sha256":"aa0d00684afd224328ae6907138865eade31f345829ebe5924d83742000c8608","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa0d00684afd224328ae6907138865eade31f345829ebe5924d83742000c8608","first_computed_at":"2026-05-18T03:21:44.123448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:44.123448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RwP/Tzbi3naA5+iyGW0ZjUysNEIa9S78cRSJDI5upciZqLydNWutTzbuIHlL1W0fYNxaSsAdcmt27akTnjJSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:44.124236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56a486efdce7b05419bdd856079764fc2dbcc9b88079d253cdd389b94d4b387e","sha256:80cee5f4204d2283015034c0c003bcd43d3bcb3f4b59e8a7252a8883f339e132"],"state_sha256":"b56d3fa16bdac8be483d1e2f7c6d5eca5d07809421de7c2f282868b22f9540c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXOUA52F0ppI0ww2JDEK+mYa+Be9/SSdYTOVlk6QZjM2T8xAPZdR0m1lUyZiIZJM3MSdi2HZLuLkW/Rs54VaDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:29:14.204913Z","bundle_sha256":"ef7c0b4a036c2b32dd32a2abde30cb5e89275b4e78e8fde0896dcff63cba45d7"}}