{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:ZNBGXZBQO5YV3XPTMS33FID3ZU","short_pith_number":"pith:ZNBGXZBQ","canonical_record":{"source":{"id":"2211.09870","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-17T20:20:47Z","cross_cats_sorted":[],"title_canon_sha256":"68031f341b94383a8d2056829d0e6200cbc2ca97582f1fa21da461dca1353f1d","abstract_canon_sha256":"d76af58e21fddf51e00204baf857e10a489815afc4867b92efc29472fd20ded5"},"schema_version":"1.0"},"canonical_sha256":"cb426be43077715dddf364b7b2a07bcd1c5dd73b2d70697de6ed0622b8f6539b","source":{"kind":"arxiv","id":"2211.09870","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.09870","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"2211.09870v1","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.09870","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZNBGXZBQO5YV","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"pith_short_16","alias_value":"ZNBGXZBQO5YV3XPT","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"pith_short_8","alias_value":"ZNBGXZBQ","created_at":"2026-07-05T05:17:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:ZNBGXZBQO5YV3XPTMS33FID3ZU","target":"record","payload":{"canonical_record":{"source":{"id":"2211.09870","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-17T20:20:47Z","cross_cats_sorted":[],"title_canon_sha256":"68031f341b94383a8d2056829d0e6200cbc2ca97582f1fa21da461dca1353f1d","abstract_canon_sha256":"d76af58e21fddf51e00204baf857e10a489815afc4867b92efc29472fd20ded5"},"schema_version":"1.0"},"canonical_sha256":"cb426be43077715dddf364b7b2a07bcd1c5dd73b2d70697de6ed0622b8f6539b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:14.973522Z","signature_b64":"bSxL08TfuCwc0MH+j345ENH0BQNiz6T1pplhzam4noGwYjoSyAW7V1QX7GeNUb1T7f2Wh0VUuGFuwJpR1mj0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb426be43077715dddf364b7b2a07bcd1c5dd73b2d70697de6ed0622b8f6539b","last_reissued_at":"2026-07-05T05:17:14.973109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:14.973109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.09870","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/tgqdab6u2C+jnEkhE/rlku6efeSGj3pXSFF/fpZ4tHdfLHBUezgLOvk0FXtZg5fdfyXUT9aRk9/c0d5IC0JBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:10:58.847192Z"},"content_sha256":"687a47f94fe79c37391146e2ed8e4012a4e192dcab75568a34201d07356e3671","schema_version":"1.0","event_id":"sha256:687a47f94fe79c37391146e2ed8e4012a4e192dcab75568a34201d07356e3671"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:ZNBGXZBQO5YV3XPTMS33FID3ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Graph Density Domination Exponent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cynthia Stoner","submitted_at":"2022-11-17T20:20:47Z","abstract_excerpt":"For graphs $G$ and $H$, what relations can be determined between $t(G,W)$ and $t(H,W)$ for a general graph $W$? We study this problem through the framework of the density domination exponent, which is defined to be the smallest constant $c$ such that $t(G,W)\\ge t(H,W)^c$ for every graph $W$. This broad generalization encompasses the Sidorenko conjecture, the Erd\\H{o}s-Simonovits Theorem on paths, and a variety of other statements relating graph homomorphism densities. We introduce some general tools for estimating the density domination exponent, and extend previous results to new graph regime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09870","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/2211.09870/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZByYJhy9FgWghhKJylpZbn7s1QSKeoTuPkm9hGq3nUM0gzWuHHYH0fvw6FfCpMyWc8U6P2np66trrhNlgGkpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:10:58.847736Z"},"content_sha256":"3514cc9fbe8ba025338a13725e513e964001244e67479b185ae6428c25c756b5","schema_version":"1.0","event_id":"sha256:3514cc9fbe8ba025338a13725e513e964001244e67479b185ae6428c25c756b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU/bundle.json","state_url":"https://pith.science/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T07:10:58Z","links":{"resolver":"https://pith.science/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU","bundle":"https://pith.science/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU/bundle.json","state":"https://pith.science/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNBGXZBQO5YV3XPTMS33FID3ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ZNBGXZBQO5YV3XPTMS33FID3ZU","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":"d76af58e21fddf51e00204baf857e10a489815afc4867b92efc29472fd20ded5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-17T20:20:47Z","title_canon_sha256":"68031f341b94383a8d2056829d0e6200cbc2ca97582f1fa21da461dca1353f1d"},"schema_version":"1.0","source":{"id":"2211.09870","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.09870","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"2211.09870v1","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.09870","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZNBGXZBQO5YV","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"pith_short_16","alias_value":"ZNBGXZBQO5YV3XPT","created_at":"2026-07-05T05:17:14Z"},{"alias_kind":"pith_short_8","alias_value":"ZNBGXZBQ","created_at":"2026-07-05T05:17:14Z"}],"graph_snapshots":[{"event_id":"sha256:3514cc9fbe8ba025338a13725e513e964001244e67479b185ae6428c25c756b5","target":"graph","created_at":"2026-07-05T05:17:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.09870/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For graphs $G$ and $H$, what relations can be determined between $t(G,W)$ and $t(H,W)$ for a general graph $W$? We study this problem through the framework of the density domination exponent, which is defined to be the smallest constant $c$ such that $t(G,W)\\ge t(H,W)^c$ for every graph $W$. This broad generalization encompasses the Sidorenko conjecture, the Erd\\H{o}s-Simonovits Theorem on paths, and a variety of other statements relating graph homomorphism densities. We introduce some general tools for estimating the density domination exponent, and extend previous results to new graph regime","authors_text":"Cynthia Stoner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-17T20:20:47Z","title":"The Graph Density Domination Exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09870","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":"sha256:687a47f94fe79c37391146e2ed8e4012a4e192dcab75568a34201d07356e3671","target":"record","created_at":"2026-07-05T05:17:14Z","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":"d76af58e21fddf51e00204baf857e10a489815afc4867b92efc29472fd20ded5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-17T20:20:47Z","title_canon_sha256":"68031f341b94383a8d2056829d0e6200cbc2ca97582f1fa21da461dca1353f1d"},"schema_version":"1.0","source":{"id":"2211.09870","kind":"arxiv","version":1}},"canonical_sha256":"cb426be43077715dddf364b7b2a07bcd1c5dd73b2d70697de6ed0622b8f6539b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb426be43077715dddf364b7b2a07bcd1c5dd73b2d70697de6ed0622b8f6539b","first_computed_at":"2026-07-05T05:17:14.973109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:17:14.973109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bSxL08TfuCwc0MH+j345ENH0BQNiz6T1pplhzam4noGwYjoSyAW7V1QX7GeNUb1T7f2Wh0VUuGFuwJpR1mj0Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:17:14.973522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.09870","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:687a47f94fe79c37391146e2ed8e4012a4e192dcab75568a34201d07356e3671","sha256:3514cc9fbe8ba025338a13725e513e964001244e67479b185ae6428c25c756b5"],"state_sha256":"d17f7ee207bf175a40dac45eab10d0a0a0ea197705a18a45cad385ab6431446a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXQrGTIWJPcmDq+7ON/DY8m+9HKD1qPi22ITHW0qilFnnRhyAhMwnbkJtwFuqYsSrxSOr553bWXLOyFyTtRVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:10:58.851441Z","bundle_sha256":"e286a309a35952651fc87fd140336ebd9c42ecd444faf72cfd0f632fcaf30410"}}