{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7QEYOH2MLBHFCTFROLOJOQ4CF4","short_pith_number":"pith:7QEYOH2M","canonical_record":{"source":{"id":"1105.5104","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-25T18:19:51Z","cross_cats_sorted":["cs.CG","math.OC"],"title_canon_sha256":"e0aa2a7d6fea429c4f584aa6cf91a2a279a1a8079b8169ab96de9bafa9ee14e6","abstract_canon_sha256":"539771b22610b04b32ab58c6b5016efabc48367ec3c68a318008aa876db71804"},"schema_version":"1.0"},"canonical_sha256":"fc09871f4c584e514cb172dc9743822f216136b228e9c00cefdefb4b97461dd4","source":{"kind":"arxiv","id":"1105.5104","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5104","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5104v3","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5104","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"7QEYOH2MLBHF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7QEYOH2MLBHFCTFR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7QEYOH2M","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7QEYOH2MLBHFCTFROLOJOQ4CF4","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5104","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-25T18:19:51Z","cross_cats_sorted":["cs.CG","math.OC"],"title_canon_sha256":"e0aa2a7d6fea429c4f584aa6cf91a2a279a1a8079b8169ab96de9bafa9ee14e6","abstract_canon_sha256":"539771b22610b04b32ab58c6b5016efabc48367ec3c68a318008aa876db71804"},"schema_version":"1.0"},"canonical_sha256":"fc09871f4c584e514cb172dc9743822f216136b228e9c00cefdefb4b97461dd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:41.502839Z","signature_b64":"Co6bk0fQBRTgbs+Haz9Qyu4EpdcetKTAVU1IpaoDeYdB9bSynBW37gtzB2K2HWtzjEh9gksXRQ1sDLpABfXMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc09871f4c584e514cb172dc9743822f216136b228e9c00cefdefb4b97461dd4","last_reissued_at":"2026-05-18T03:07:41.502299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:41.502299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5104","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":"2026-05-18T03:07:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ka2RRSP85WW4KUFOLFdRf4xFrVSMAPE2s95ljWI+V+h6DHzhHUWnyNfEpAB3BJxsC76uZmi4P4tRvLNiqdDMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T05:29:22.348956Z"},"content_sha256":"2ab3a250f5e127d2caaf03273ff44bbf8a089b61213677a51ec3ce0dde5925ae","schema_version":"1.0","event_id":"sha256:2ab3a250f5e127d2caaf03273ff44bbf8a089b61213677a51ec3ce0dde5925ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7QEYOH2MLBHFCTFROLOJOQ4CF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplicial Flat Norm with Scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.OC"],"primary_cat":"math.DG","authors_text":"Bala Krishnamoorthy, Kevin R. Vixie, Sharif Ibrahim","submitted_at":"2011-05-25T18:19:51Z","abstract_excerpt":"We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the multiscale simplicial flat norm as an instance of integer linear optimization. Following recent results on related problems, the multiscale simplicial flat norm integer program can be solved in polynomial time by solving its linear programming relaxation, when the simplicial complex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5104","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":"2026-05-18T03:07:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwTV7dJQAr4yKOkwmih+oPH7uRfLIrxCWHDlAzT3U7LgCSSEj3PXoctYFCU6TO+0+t5VtcsuUEwXFyfzGYwYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T05:29:22.349304Z"},"content_sha256":"8d3ee16ca5918fcfc288eb4c729c527b189fd167ffd350898b229607102d9e4c","schema_version":"1.0","event_id":"sha256:8d3ee16ca5918fcfc288eb4c729c527b189fd167ffd350898b229607102d9e4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4/bundle.json","state_url":"https://pith.science/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4/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":"2026-06-30T05:29:22Z","links":{"resolver":"https://pith.science/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4","bundle":"https://pith.science/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4/bundle.json","state":"https://pith.science/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QEYOH2MLBHFCTFROLOJOQ4CF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7QEYOH2MLBHFCTFROLOJOQ4CF4","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":"539771b22610b04b32ab58c6b5016efabc48367ec3c68a318008aa876db71804","cross_cats_sorted":["cs.CG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-25T18:19:51Z","title_canon_sha256":"e0aa2a7d6fea429c4f584aa6cf91a2a279a1a8079b8169ab96de9bafa9ee14e6"},"schema_version":"1.0","source":{"id":"1105.5104","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5104","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5104v3","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5104","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"7QEYOH2MLBHF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7QEYOH2MLBHFCTFR","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7QEYOH2M","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:8d3ee16ca5918fcfc288eb4c729c527b189fd167ffd350898b229607102d9e4c","target":"graph","created_at":"2026-05-18T03:07:41Z","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 multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the multiscale simplicial flat norm as an instance of integer linear optimization. Following recent results on related problems, the multiscale simplicial flat norm integer program can be solved in polynomial time by solving its linear programming relaxation, when the simplicial complex","authors_text":"Bala Krishnamoorthy, Kevin R. Vixie, Sharif Ibrahim","cross_cats":["cs.CG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-25T18:19:51Z","title":"Simplicial Flat Norm with Scale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5104","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":"sha256:2ab3a250f5e127d2caaf03273ff44bbf8a089b61213677a51ec3ce0dde5925ae","target":"record","created_at":"2026-05-18T03:07:41Z","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":"539771b22610b04b32ab58c6b5016efabc48367ec3c68a318008aa876db71804","cross_cats_sorted":["cs.CG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-25T18:19:51Z","title_canon_sha256":"e0aa2a7d6fea429c4f584aa6cf91a2a279a1a8079b8169ab96de9bafa9ee14e6"},"schema_version":"1.0","source":{"id":"1105.5104","kind":"arxiv","version":3}},"canonical_sha256":"fc09871f4c584e514cb172dc9743822f216136b228e9c00cefdefb4b97461dd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc09871f4c584e514cb172dc9743822f216136b228e9c00cefdefb4b97461dd4","first_computed_at":"2026-05-18T03:07:41.502299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:41.502299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Co6bk0fQBRTgbs+Haz9Qyu4EpdcetKTAVU1IpaoDeYdB9bSynBW37gtzB2K2HWtzjEh9gksXRQ1sDLpABfXMAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:41.502839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5104","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ab3a250f5e127d2caaf03273ff44bbf8a089b61213677a51ec3ce0dde5925ae","sha256:8d3ee16ca5918fcfc288eb4c729c527b189fd167ffd350898b229607102d9e4c"],"state_sha256":"1908691bec82511c85cedad54bbf40d3046b05f6646c1831ef74ca1f6127e6cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fW8puu595gYIuSLfydhThpLcV/ydoxUB3rvo01/PHu7saiG+szYBED8jq3EsbKMzupfGYZvJKFcptOo33QTJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T05:29:22.351890Z","bundle_sha256":"96349ce7e1df6df470247c688888b9dfd2463384fc07077c20173554e386a0e6"}}