{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XKXCDG3TZABNNXUGFSCQEAZ774","short_pith_number":"pith:XKXCDG3T","schema_version":"1.0","canonical_sha256":"baae219b73c802d6de862c8502033fff2b358becafd1ed592de69d5dd7341c04","source":{"kind":"arxiv","id":"2607.14718","version":1},"attestation_state":"computed","paper":{"title":"Anchored Nash inequalities and heat kernel bounds for a class of random conductance models with long-range jumps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Kun Yin, Martin Slowik, Sebastian Andres, Xin Chen","submitted_at":"2026-07-16T08:35:48Z","abstract_excerpt":"We show anchored versions of the Nash inequality for discrete non-local divergence-form operators with degenerate weights. They allow to control the $L^{2}$-norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide on-diagonal heat kernel upper bounds for a class of random conductance models with degenerate jump rates allowing long-range jumps. The results are established on a class of graphs including the integer lattice and possibly correlated supercritical percolation clusters."},"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":"2607.14718","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-16T08:35:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3e0bfcdf395470c938c2c9408d2fd1d3388f632c046e843f3df1d6192d8f1282","abstract_canon_sha256":"efcf8824fd75dcc61f33680ba68fd5b200886ffef34d59404d414756f4ed3e9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:27.338033Z","signature_b64":"nuIjENcQ59dElJWl1jCDUhhD/jRQAC00c3LA5XKnEUjT/h//OWGuhe2xXfZMpaDCDXyWI11IICEIlRqK8IuKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baae219b73c802d6de862c8502033fff2b358becafd1ed592de69d5dd7341c04","last_reissued_at":"2026-07-17T01:21:27.337154Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:27.337154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anchored Nash inequalities and heat kernel bounds for a class of random conductance models with long-range jumps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Kun Yin, Martin Slowik, Sebastian Andres, Xin Chen","submitted_at":"2026-07-16T08:35:48Z","abstract_excerpt":"We show anchored versions of the Nash inequality for discrete non-local divergence-form operators with degenerate weights. They allow to control the $L^{2}$-norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide on-diagonal heat kernel upper bounds for a class of random conductance models with degenerate jump rates allowing long-range jumps. The results are established on a class of graphs including the integer lattice and possibly correlated supercritical percolation clusters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14718","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/2607.14718/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":"2607.14718","created_at":"2026-07-17T01:21:27.337606+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.14718v1","created_at":"2026-07-17T01:21:27.337606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14718","created_at":"2026-07-17T01:21:27.337606+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKXCDG3TZABN","created_at":"2026-07-17T01:21:27.337606+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKXCDG3TZABNNXUG","created_at":"2026-07-17T01:21:27.337606+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKXCDG3T","created_at":"2026-07-17T01:21:27.337606+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/XKXCDG3TZABNNXUGFSCQEAZ774","json":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774.json","graph_json":"https://pith.science/api/pith-number/XKXCDG3TZABNNXUGFSCQEAZ774/graph.json","events_json":"https://pith.science/api/pith-number/XKXCDG3TZABNNXUGFSCQEAZ774/events.json","paper":"https://pith.science/paper/XKXCDG3T"},"agent_actions":{"view_html":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774","download_json":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774.json","view_paper":"https://pith.science/paper/XKXCDG3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.14718&json=true","fetch_graph":"https://pith.science/api/pith-number/XKXCDG3TZABNNXUGFSCQEAZ774/graph.json","fetch_events":"https://pith.science/api/pith-number/XKXCDG3TZABNNXUGFSCQEAZ774/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774/action/storage_attestation","attest_author":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774/action/author_attestation","sign_citation":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774/action/citation_signature","submit_replication":"https://pith.science/pith/XKXCDG3TZABNNXUGFSCQEAZ774/action/replication_record"}},"created_at":"2026-07-17T01:21:27.337606+00:00","updated_at":"2026-07-17T01:21:27.337606+00:00"}