{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TK6W5TV6IHL3HMTEJR63QB334M","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":"da102c1e63e40060316046841569c5ea1d80b5bec2c5c64ddf93e446642f5a51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-09T21:49:46Z","title_canon_sha256":"98b680c2c293cad3e12596b0c977cb87887c11eb38d9fa155842dcff7edfbea2"},"schema_version":"1.0","source":{"id":"1811.04145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04145","created_at":"2026-05-18T00:01:06Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04145v1","created_at":"2026-05-18T00:01:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04145","created_at":"2026-05-18T00:01:06Z"},{"alias_kind":"pith_short_12","alias_value":"TK6W5TV6IHL3","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TK6W5TV6IHL3HMTE","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TK6W5TV6","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:6cbfd31e2e304f941116c0d0de3d157cbb090d912a88938f7f9673eb54f32b9f","target":"graph","created_at":"2026-05-18T00:01:06Z","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 show how to extend the Covering Spectrum (CS) of Sormani-Wei to two spectra, called the Extended Covering Spectrum (ECS) and Entourage Spectrum (ES) that are new for Riemannian manifolds but defined with useful properties on any metric on a Peano continuum. We do so by measuring in two different ways the \"size\" of a topological generalization of the $\\delta$-covers of Sormani-Wei called \"entourage covers\". For Riemannian manifolds $M$ of dimension at least 3, we characterize entourage covers as those covers corresponding to the normal closures of finite subsets of $\\pi_{1}(M)$. We show that","authors_text":"Conrad Plaut","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-09T21:49:46Z","title":"Spectra related to the length spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04145","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":"sha256:944fe0aed2e486e56624c2b33f68733e5d3ea5a7b66f46dc829b39b49b71f20f","target":"record","created_at":"2026-05-18T00:01:06Z","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":"da102c1e63e40060316046841569c5ea1d80b5bec2c5c64ddf93e446642f5a51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-09T21:49:46Z","title_canon_sha256":"98b680c2c293cad3e12596b0c977cb87887c11eb38d9fa155842dcff7edfbea2"},"schema_version":"1.0","source":{"id":"1811.04145","kind":"arxiv","version":1}},"canonical_sha256":"9abd6ecebe41d7b3b2644c7db8077be306dbb6fd06d520b8961401fdd097e6d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9abd6ecebe41d7b3b2644c7db8077be306dbb6fd06d520b8961401fdd097e6d3","first_computed_at":"2026-05-18T00:01:06.205226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:06.205226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kSZgCmYCGWsIJOrzno7FdxwcjYj15hdbc2kyoNO6mTpb4emysdRtazL97GgD9w34MREF/xxR4xjD2k/5OMckDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:06.205868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:944fe0aed2e486e56624c2b33f68733e5d3ea5a7b66f46dc829b39b49b71f20f","sha256:6cbfd31e2e304f941116c0d0de3d157cbb090d912a88938f7f9673eb54f32b9f"],"state_sha256":"a69417b9c603c9e3c97ea814c5305c513a5ac8e321f47885a77e5595c1aef937"}