{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OBPFYRYDCXB5JF6QWTHY2MA4BV","short_pith_number":"pith:OBPFYRYD","schema_version":"1.0","canonical_sha256":"705e5c470315c3d497d0b4cf8d301c0d776b28f7b8e1d8a5f8b7f3016cada21e","source":{"kind":"arxiv","id":"2407.13502","version":1},"attestation_state":"computed","paper":{"title":"Spectra of Poisson functionals and applications in continuum percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chinmoy Bhattacharjee, D. Yogeshwaran, Giovanni Peccati","submitted_at":"2024-07-18T13:33:57Z","abstract_excerpt":"Let $\\eta$ be a Poisson random measure (defined on some Polish space), and let $F(\\eta)$ be a square-integrable functional of $\\eta$. In this paper we define and study a new notion of {\\it spectral point process} associated with $F(\\eta)$, and use such an object to study sharp noise instability and sensitivity properties of planar critical continuum percolation models under spatial birth-death (Ornstein-Uhlenbeck) dynamics -- the notion of sharp noise instability being a natural strengthening of the absence of noise stability. The concept of spectral point process is defined by exploiting the "},"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":"2407.13502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-18T13:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"71a300491d6d5346b14fd4da333f6ab132041e3aa32bd76aecaead781ca60b68","abstract_canon_sha256":"0749ce2ae0c263626f390abfaca97e6d4009e296eb9eb73d46fd7adfe476ca04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:45:39.860073Z","signature_b64":"OqfIUfG+KLWt899KkuP/oWvUQ0AdzG5LI6XupE6RQBSoARcjP3fFva3aqDpktT6rVs1gZnItDVNd0nYlzwE5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"705e5c470315c3d497d0b4cf8d301c0d776b28f7b8e1d8a5f8b7f3016cada21e","last_reissued_at":"2026-07-05T08:45:39.859671Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:45:39.859671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectra of Poisson functionals and applications in continuum percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chinmoy Bhattacharjee, D. Yogeshwaran, Giovanni Peccati","submitted_at":"2024-07-18T13:33:57Z","abstract_excerpt":"Let $\\eta$ be a Poisson random measure (defined on some Polish space), and let $F(\\eta)$ be a square-integrable functional of $\\eta$. In this paper we define and study a new notion of {\\it spectral point process} associated with $F(\\eta)$, and use such an object to study sharp noise instability and sensitivity properties of planar critical continuum percolation models under spatial birth-death (Ornstein-Uhlenbeck) dynamics -- the notion of sharp noise instability being a natural strengthening of the absence of noise stability. The concept of spectral point process is defined by exploiting the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.13502/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2407.13502","created_at":"2026-07-05T08:45:39.859727+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.13502v1","created_at":"2026-07-05T08:45:39.859727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.13502","created_at":"2026-07-05T08:45:39.859727+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBPFYRYDCXB5","created_at":"2026-07-05T08:45:39.859727+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBPFYRYDCXB5JF6Q","created_at":"2026-07-05T08:45:39.859727+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBPFYRYD","created_at":"2026-07-05T08:45:39.859727+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.10379","citing_title":"Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV","json":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV.json","graph_json":"https://pith.science/api/pith-number/OBPFYRYDCXB5JF6QWTHY2MA4BV/graph.json","events_json":"https://pith.science/api/pith-number/OBPFYRYDCXB5JF6QWTHY2MA4BV/events.json","paper":"https://pith.science/paper/OBPFYRYD"},"agent_actions":{"view_html":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV","download_json":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV.json","view_paper":"https://pith.science/paper/OBPFYRYD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.13502&json=true","fetch_graph":"https://pith.science/api/pith-number/OBPFYRYDCXB5JF6QWTHY2MA4BV/graph.json","fetch_events":"https://pith.science/api/pith-number/OBPFYRYDCXB5JF6QWTHY2MA4BV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV/action/storage_attestation","attest_author":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV/action/author_attestation","sign_citation":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV/action/citation_signature","submit_replication":"https://pith.science/pith/OBPFYRYDCXB5JF6QWTHY2MA4BV/action/replication_record"}},"created_at":"2026-07-05T08:45:39.859727+00:00","updated_at":"2026-07-05T08:45:39.859727+00:00"}