{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:75CIGB46PFETLJJ7K6UY44ZZ55","short_pith_number":"pith:75CIGB46","schema_version":"1.0","canonical_sha256":"ff4483079e794935a53f57a98e7339ef47428437127c2da12cc503f9871453b9","source":{"kind":"arxiv","id":"1603.08113","version":3},"attestation_state":"computed","paper":{"title":"Reconstructing undirected graphs from eigenspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Paul Rochet, Thibault Espinasse, Yohann De Castro","submitted_at":"2016-03-26T14:56:35Z","abstract_excerpt":"In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs or for Markov chains observed at random times. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator $\\mathsf{A} \\mathsf{B}-\\mathsf{B} \\mathsf{A}$ between symmetric matrices $\\mathsf{A}$ and $\\mathsf{B}$.\n  In the Erd\\H{o}s-R\\'enyi model with no self-loops, we show that identifiability (i.e., the ability to reconst"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.08113","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-26T14:56:35Z","cross_cats_sorted":["cs.IT","math.IT","stat.ME","stat.ML","stat.TH"],"title_canon_sha256":"415d125767bd1f27a82ef7a5b6c0505e7df5a2f3e74e9e844239475d1dca4716","abstract_canon_sha256":"70a30f7db18adab56d27f5effceb13bb98dd79f9dc3c32e8876d6f09a4cbcbf5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:42.927576Z","signature_b64":"soTJSdJJEmleI8Ti7CCwQ/4mRj1qssMM5ZNG+57MidksPvI1Ker6ZrEvyMOhZhlf9LJK7ZFsEhFDPM3N4w/TDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff4483079e794935a53f57a98e7339ef47428437127c2da12cc503f9871453b9","last_reissued_at":"2026-05-18T00:48:42.927156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:42.927156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconstructing undirected graphs from eigenspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Paul Rochet, Thibault Espinasse, Yohann De Castro","submitted_at":"2016-03-26T14:56:35Z","abstract_excerpt":"In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs or for Markov chains observed at random times. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator $\\mathsf{A} \\mathsf{B}-\\mathsf{B} \\mathsf{A}$ between symmetric matrices $\\mathsf{A}$ and $\\mathsf{B}$.\n  In the Erd\\H{o}s-R\\'enyi model with no self-loops, we show that identifiability (i.e., the ability to reconst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08113","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.08113","created_at":"2026-05-18T00:48:42.927227+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08113v3","created_at":"2026-05-18T00:48:42.927227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08113","created_at":"2026-05-18T00:48:42.927227+00:00"},{"alias_kind":"pith_short_12","alias_value":"75CIGB46PFET","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"75CIGB46PFETLJJ7","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"75CIGB46","created_at":"2026-05-18T12:30:04.600751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55","json":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55.json","graph_json":"https://pith.science/api/pith-number/75CIGB46PFETLJJ7K6UY44ZZ55/graph.json","events_json":"https://pith.science/api/pith-number/75CIGB46PFETLJJ7K6UY44ZZ55/events.json","paper":"https://pith.science/paper/75CIGB46"},"agent_actions":{"view_html":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55","download_json":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55.json","view_paper":"https://pith.science/paper/75CIGB46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08113&json=true","fetch_graph":"https://pith.science/api/pith-number/75CIGB46PFETLJJ7K6UY44ZZ55/graph.json","fetch_events":"https://pith.science/api/pith-number/75CIGB46PFETLJJ7K6UY44ZZ55/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55/action/storage_attestation","attest_author":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55/action/author_attestation","sign_citation":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55/action/citation_signature","submit_replication":"https://pith.science/pith/75CIGB46PFETLJJ7K6UY44ZZ55/action/replication_record"}},"created_at":"2026-05-18T00:48:42.927227+00:00","updated_at":"2026-05-18T00:48:42.927227+00:00"}