{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZPWX5BWLPJT55FT4JZISUQWIVG","short_pith_number":"pith:ZPWX5BWL","canonical_record":{"source":{"id":"2607.27162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T17:38:12Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"301a28f9581e9419addb7f937b3f03bc4bb70c2ee9602328e4d31fe37c93a46f","abstract_canon_sha256":"a81bfc3505d1e33da2943e27bf64cc62fdf11994e0cbe9b4f2017bfcdf3d1b66"},"schema_version":"1.0"},"canonical_sha256":"cbed7e86cb7a67de967c4e512a42c8a9805862bbf527efc50478da851024a0c1","source":{"kind":"arxiv","id":"2607.27162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27162","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27162v1","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27162","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZPWX5BWLPJT5","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZPWX5BWLPJT55FT4","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZPWX5BWL","created_at":"2026-07-30T01:23:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZPWX5BWLPJT55FT4JZISUQWIVG","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T17:38:12Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"301a28f9581e9419addb7f937b3f03bc4bb70c2ee9602328e4d31fe37c93a46f","abstract_canon_sha256":"a81bfc3505d1e33da2943e27bf64cc62fdf11994e0cbe9b4f2017bfcdf3d1b66"},"schema_version":"1.0"},"canonical_sha256":"cbed7e86cb7a67de967c4e512a42c8a9805862bbf527efc50478da851024a0c1","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbed7e86cb7a67de967c4e512a42c8a9805862bbf527efc50478da851024a0c1","last_reissued_at":"2026-07-30T01:23:55.085708Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:23:55.085708Z"},"source_kind":"arxiv","source_id":"2607.27162","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":"2026-07-30T01:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pyv7OkiyJ0Z+maawn88xmt5RPczxN9tCp0merCN53+Rs3xRp4xbJVb0GUW3fndtVm/ik2taxeXuZItuQZF79Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:30:44.610914Z"},"content_sha256":"546916b9bec769fa3903ad5af190043f167f0901d2adb26ee2973a52f5f41201","schema_version":"1.0","event_id":"sha256:546916b9bec769fa3903ad5af190043f167f0901d2adb26ee2973a52f5f41201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZPWX5BWLPJT55FT4JZISUQWIVG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointwise subexponential growth and near-diffusive displacement on bounded-degree graphs with non-negative Ollivier--Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.DG","authors_text":"Chiyu Zhou","submitted_at":"2026-07-29T17:38:12Z","abstract_excerpt":"Let $G=(V,E)$ be a possibly infinite, locally finite graph with non-negative Ollivier--Ricci curvature and degrees bounded by $d<\\infty$. We prove that there exists a constant $C_d$ such that the continuous-time random walk displacement and log-volume growth satisfy \\[ \\mathbb{E}_x \\mathrm{dist}(x,X_t)^2 \\le t \\exp\\left[C_d \\sqrt{\\log t \\log\\log t}\\right], \\] \\[ \\log \\mathrm{Vol}(B(x,r)) \\le \\exp\\left[C_d \\sqrt{\\log r \\log\\log r}\\right], \\] for every $x\\in V$ and all $r,t \\ge e^e$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27162","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/2607.27162/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":"2026-07-30T01:23:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TtR/z/95Mfjoukk7VH63Dr6BtePEEojZtRboRXXbd1/9/gwftik9H3AuyfIpbcwqK/qWrpx5D699Sc3kvkXaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:30:44.611457Z"},"content_sha256":"b52e8970ee444a1b0ae90cd285e0193d0f842c0daeb0b3b873249f0c1ff0c373","schema_version":"1.0","event_id":"sha256:b52e8970ee444a1b0ae90cd285e0193d0f842c0daeb0b3b873249f0c1ff0c373"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPWX5BWLPJT55FT4JZISUQWIVG/bundle.json","state_url":"https://pith.science/pith/ZPWX5BWLPJT55FT4JZISUQWIVG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPWX5BWLPJT55FT4JZISUQWIVG/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":"2026-08-21T00:30:44Z","links":{"resolver":"https://pith.science/pith/ZPWX5BWLPJT55FT4JZISUQWIVG","bundle":"https://pith.science/pith/ZPWX5BWLPJT55FT4JZISUQWIVG/bundle.json","state":"https://pith.science/pith/ZPWX5BWLPJT55FT4JZISUQWIVG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPWX5BWLPJT55FT4JZISUQWIVG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZPWX5BWLPJT55FT4JZISUQWIVG","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":"a81bfc3505d1e33da2943e27bf64cc62fdf11994e0cbe9b4f2017bfcdf3d1b66","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T17:38:12Z","title_canon_sha256":"301a28f9581e9419addb7f937b3f03bc4bb70c2ee9602328e4d31fe37c93a46f"},"schema_version":"1.0","source":{"id":"2607.27162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27162","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27162v1","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27162","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZPWX5BWLPJT5","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZPWX5BWLPJT55FT4","created_at":"2026-07-30T01:23:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZPWX5BWL","created_at":"2026-07-30T01:23:55Z"}],"graph_snapshots":[{"event_id":"sha256:b52e8970ee444a1b0ae90cd285e0193d0f842c0daeb0b3b873249f0c1ff0c373","target":"graph","created_at":"2026-07-30T01:23:55Z","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/2607.27162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G=(V,E)$ be a possibly infinite, locally finite graph with non-negative Ollivier--Ricci curvature and degrees bounded by $d<\\infty$. We prove that there exists a constant $C_d$ such that the continuous-time random walk displacement and log-volume growth satisfy \\[ \\mathbb{E}_x \\mathrm{dist}(x,X_t)^2 \\le t \\exp\\left[C_d \\sqrt{\\log t \\log\\log t}\\right], \\] \\[ \\log \\mathrm{Vol}(B(x,r)) \\le \\exp\\left[C_d \\sqrt{\\log r \\log\\log r}\\right], \\] for every $x\\in V$ and all $r,t \\ge e^e$.","authors_text":"Chiyu Zhou","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T17:38:12Z","title":"Pointwise subexponential growth and near-diffusive displacement on bounded-degree graphs with non-negative Ollivier--Ricci curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27162","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":"sha256:546916b9bec769fa3903ad5af190043f167f0901d2adb26ee2973a52f5f41201","target":"record","created_at":"2026-07-30T01:23:55Z","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":"a81bfc3505d1e33da2943e27bf64cc62fdf11994e0cbe9b4f2017bfcdf3d1b66","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T17:38:12Z","title_canon_sha256":"301a28f9581e9419addb7f937b3f03bc4bb70c2ee9602328e4d31fe37c93a46f"},"schema_version":"1.0","source":{"id":"2607.27162","kind":"arxiv","version":1}},"canonical_sha256":"cbed7e86cb7a67de967c4e512a42c8a9805862bbf527efc50478da851024a0c1","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbed7e86cb7a67de967c4e512a42c8a9805862bbf527efc50478da851024a0c1","first_computed_at":"2026-07-30T01:23:55.085708Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:23:55.085708Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:546916b9bec769fa3903ad5af190043f167f0901d2adb26ee2973a52f5f41201","sha256:b52e8970ee444a1b0ae90cd285e0193d0f842c0daeb0b3b873249f0c1ff0c373"],"state_sha256":"373d93641d3a44e27d05d655a908d58c23cb8974567173dfa34e1002c80aec32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLBWihbbaS6zJYChT1YlEIYY+Y7aT7WVO+XgokJEP3KDB5f/3VFcyqpDY4+RuOzoCk5tH/SfJcmusqDvLZgqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T00:30:44.617077Z","bundle_sha256":"3df9690a8123d74a9724ea491c2c3d96c6a6cd0822a3e536dae68dd79fbdeee0"}}