{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BPUEDLNR5SXLOFMWTJG32N5Y4I","short_pith_number":"pith:BPUEDLNR","canonical_record":{"source":{"id":"1703.03632","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-10T11:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"52e7fda1df897555a7cfc14b7feb8112b990a22a4abd49d74c7c7d6b86ef8de0","abstract_canon_sha256":"6e6f8bea66352eb13ac6ac8d9861729a3a2b1a13fbd575165eeb155e5de72dea"},"schema_version":"1.0"},"canonical_sha256":"0be841adb1ecaeb715969a4dbd37b8e234c9ef24ceb21024a6bb29642160c1a8","source":{"kind":"arxiv","id":"1703.03632","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03632","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03632v3","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03632","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"BPUEDLNR5SXL","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"pith_short_16","alias_value":"BPUEDLNR5SXLOFMW","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"pith_short_8","alias_value":"BPUEDLNR","created_at":"2026-07-05T02:31:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BPUEDLNR5SXLOFMWTJG32N5Y4I","target":"record","payload":{"canonical_record":{"source":{"id":"1703.03632","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-10T11:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"52e7fda1df897555a7cfc14b7feb8112b990a22a4abd49d74c7c7d6b86ef8de0","abstract_canon_sha256":"6e6f8bea66352eb13ac6ac8d9861729a3a2b1a13fbd575165eeb155e5de72dea"},"schema_version":"1.0"},"canonical_sha256":"0be841adb1ecaeb715969a4dbd37b8e234c9ef24ceb21024a6bb29642160c1a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:31:57.231377Z","signature_b64":"3IykN7ONp+YdnjDJVmGF0ZzBnFd/LjO16p9IvPUcImJMICLAadArT3t3qUgNehKHXEBeng4zJkrxZc3G2/m2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0be841adb1ecaeb715969a4dbd37b8e234c9ef24ceb21024a6bb29642160c1a8","last_reissued_at":"2026-07-05T02:31:57.230905Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:31:57.230905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.03632","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":"2026-07-05T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nd7znBExnNtXZCbo7F1zlvYk7pIYq/Cv19lqWdBLZdH2DgeqzmcDnowmfQTtOkHjnlQQzti/mQ887MIXlkC+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:58:34.714611Z"},"content_sha256":"901993c8a48e2abc4234c1fad49b59f8ef74eed8b5c1bacb971b5908df632257","schema_version":"1.0","event_id":"sha256:901993c8a48e2abc4234c1fad49b59f8ef74eed8b5c1bacb971b5908df632257"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BPUEDLNR5SXLOFMWTJG32N5Y4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable Invariants for Multiparameter Persistence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Oliver G\\\"afvert, Wojciech Chach\\'olski","submitted_at":"2017-03-10T11:28:39Z","abstract_excerpt":"In this paper we explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03632","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1703.03632/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FqI6dpvz4oXtVPPra4bTSi7vLdm1ndLk+Ef3gRYk9HJlCCfQSPBhhQpAZBDshqbYBPENEKyrdXc5FybSj1GADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:58:34.715127Z"},"content_sha256":"126a7153fdfaa6bef7450cae3e60461810603bb906e4274b269b0767538c5290","schema_version":"1.0","event_id":"sha256:126a7153fdfaa6bef7450cae3e60461810603bb906e4274b269b0767538c5290"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I/bundle.json","state_url":"https://pith.science/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I/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":"2026-08-10T17:58:34Z","links":{"resolver":"https://pith.science/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I","bundle":"https://pith.science/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I/bundle.json","state":"https://pith.science/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPUEDLNR5SXLOFMWTJG32N5Y4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BPUEDLNR5SXLOFMWTJG32N5Y4I","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":"6e6f8bea66352eb13ac6ac8d9861729a3a2b1a13fbd575165eeb155e5de72dea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-10T11:28:39Z","title_canon_sha256":"52e7fda1df897555a7cfc14b7feb8112b990a22a4abd49d74c7c7d6b86ef8de0"},"schema_version":"1.0","source":{"id":"1703.03632","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03632","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03632v3","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03632","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"BPUEDLNR5SXL","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"pith_short_16","alias_value":"BPUEDLNR5SXLOFMW","created_at":"2026-07-05T02:31:57Z"},{"alias_kind":"pith_short_8","alias_value":"BPUEDLNR","created_at":"2026-07-05T02:31:57Z"}],"graph_snapshots":[{"event_id":"sha256:126a7153fdfaa6bef7450cae3e60461810603bb906e4274b269b0767538c5290","target":"graph","created_at":"2026-07-05T02:31:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1703.03632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard.","authors_text":"Oliver G\\\"afvert, Wojciech Chach\\'olski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-10T11:28:39Z","title":"Stable Invariants for Multiparameter Persistence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03632","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":"sha256:901993c8a48e2abc4234c1fad49b59f8ef74eed8b5c1bacb971b5908df632257","target":"record","created_at":"2026-07-05T02:31:57Z","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":"6e6f8bea66352eb13ac6ac8d9861729a3a2b1a13fbd575165eeb155e5de72dea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-10T11:28:39Z","title_canon_sha256":"52e7fda1df897555a7cfc14b7feb8112b990a22a4abd49d74c7c7d6b86ef8de0"},"schema_version":"1.0","source":{"id":"1703.03632","kind":"arxiv","version":3}},"canonical_sha256":"0be841adb1ecaeb715969a4dbd37b8e234c9ef24ceb21024a6bb29642160c1a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0be841adb1ecaeb715969a4dbd37b8e234c9ef24ceb21024a6bb29642160c1a8","first_computed_at":"2026-07-05T02:31:57.230905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:31:57.230905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3IykN7ONp+YdnjDJVmGF0ZzBnFd/LjO16p9IvPUcImJMICLAadArT3t3qUgNehKHXEBeng4zJkrxZc3G2/m2CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:31:57.231377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03632","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:901993c8a48e2abc4234c1fad49b59f8ef74eed8b5c1bacb971b5908df632257","sha256:126a7153fdfaa6bef7450cae3e60461810603bb906e4274b269b0767538c5290"],"state_sha256":"f25d1f66781ed257e1bb29024ca6afc60bcb30ecda5921afdb1007d82d61d5b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CbL0BAD2rIRQbZ/vuiLu57TSfnN7OvKPpcGLLHVne+qN5zz/4UvM/FXfVu3uaCD2CrW1XqIzCU5TtXSjHKdbBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T17:58:34.719637Z","bundle_sha256":"f522fabd8669cbf0ed8c3886d5ad6315271a73f63fffd2d4dd172cf4315aa99b"}}