{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4XPD3GXQ63WLJLDP3GHOA3F5N7","short_pith_number":"pith:4XPD3GXQ","schema_version":"1.0","canonical_sha256":"e5de3d9af0f6ecb4ac6fd98ee06cbd6ffbfcad389b908ab9d64871ff681c806d","source":{"kind":"arxiv","id":"2607.16676","version":1},"attestation_state":"computed","paper":{"title":"The Value of Depth in Message Passing on Sparse Graphs: A Kesten-Stigum Dichotomy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aseem Raj Baranwal","submitted_at":"2026-07-18T07:11:45Z","abstract_excerpt":"How deep does a graph neural network need to be on a sparse graph? We study its purest statistical form: node classification on the sparse contextual stochastic block model (CSBM) with average degree $\\Delta=O(1)$, whose local weak limit is a broadcast-labelled Poisson Galton-Watson tree. Prior work derived a message-passing classifier $h_\\ell$ that aggregates from each vertex at distance $k\\le\\ell$ the attenuated evidence $2\\operatorname{artanh}(\\gamma^k t(X_v))$, with $\\gamma$ the edge signal and $t$ a bounded likelihood-ratio transform of the feature. We prove that the value of depth is gov"},"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":"2607.16676","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-18T07:11:45Z","cross_cats_sorted":["cs.LG","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"0923b3a016ece23cecea71e451ec47a5247a1c767d6ae6ccc7062bd6ff3dd152","abstract_canon_sha256":"176b3a36071bb9021dd735aef1f82a898680e5fc930fe1448b4c6ab3690f4f2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:20:21.431615Z","signature_b64":"iusltfUubyyf6ExfCqCOBgnQ1/I5GCEbJMkJYsubUUOrBy5cGZRoc9o8NOQiTh9LoGpNHjjXiv/A2voPcRb0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5de3d9af0f6ecb4ac6fd98ee06cbd6ffbfcad389b908ab9d64871ff681c806d","last_reissued_at":"2026-07-21T01:20:21.430759Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:20:21.430759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Value of Depth in Message Passing on Sparse Graphs: A Kesten-Stigum Dichotomy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aseem Raj Baranwal","submitted_at":"2026-07-18T07:11:45Z","abstract_excerpt":"How deep does a graph neural network need to be on a sparse graph? We study its purest statistical form: node classification on the sparse contextual stochastic block model (CSBM) with average degree $\\Delta=O(1)$, whose local weak limit is a broadcast-labelled Poisson Galton-Watson tree. Prior work derived a message-passing classifier $h_\\ell$ that aggregates from each vertex at distance $k\\le\\ell$ the attenuated evidence $2\\operatorname{artanh}(\\gamma^k t(X_v))$, with $\\gamma$ the edge signal and $t$ a bounded likelihood-ratio transform of the feature. We prove that the value of depth is gov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16676","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/2607.16676/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":"2607.16676","created_at":"2026-07-21T01:20:21.431197+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.16676v1","created_at":"2026-07-21T01:20:21.431197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16676","created_at":"2026-07-21T01:20:21.431197+00:00"},{"alias_kind":"pith_short_12","alias_value":"4XPD3GXQ63WL","created_at":"2026-07-21T01:20:21.431197+00:00"},{"alias_kind":"pith_short_16","alias_value":"4XPD3GXQ63WLJLDP","created_at":"2026-07-21T01:20:21.431197+00:00"},{"alias_kind":"pith_short_8","alias_value":"4XPD3GXQ","created_at":"2026-07-21T01:20:21.431197+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/4XPD3GXQ63WLJLDP3GHOA3F5N7","json":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7.json","graph_json":"https://pith.science/api/pith-number/4XPD3GXQ63WLJLDP3GHOA3F5N7/graph.json","events_json":"https://pith.science/api/pith-number/4XPD3GXQ63WLJLDP3GHOA3F5N7/events.json","paper":"https://pith.science/paper/4XPD3GXQ"},"agent_actions":{"view_html":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7","download_json":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7.json","view_paper":"https://pith.science/paper/4XPD3GXQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.16676&json=true","fetch_graph":"https://pith.science/api/pith-number/4XPD3GXQ63WLJLDP3GHOA3F5N7/graph.json","fetch_events":"https://pith.science/api/pith-number/4XPD3GXQ63WLJLDP3GHOA3F5N7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7/action/storage_attestation","attest_author":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7/action/author_attestation","sign_citation":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7/action/citation_signature","submit_replication":"https://pith.science/pith/4XPD3GXQ63WLJLDP3GHOA3F5N7/action/replication_record"}},"created_at":"2026-07-21T01:20:21.431197+00:00","updated_at":"2026-07-21T01:20:21.431197+00:00"}