{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UZTN6BEY25OCRIWSOZIEA33AWQ","short_pith_number":"pith:UZTN6BEY","canonical_record":{"source":{"id":"2506.08810","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"62612d90e1848a00a9e5bc7aca9481cb1c7a8fea4df55cf3a648669bf326f77d","abstract_canon_sha256":"c2c2b9867696aa3abd989e3f82dc19a0f6c5b1a6deded065ea7f72a7927f57be"},"schema_version":"1.0"},"canonical_sha256":"a666df0498d75c28a2d27650406f60b40617ce41f5d58cfcd0f652c27fed035a","source":{"kind":"arxiv","id":"2506.08810","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08810","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08810v3","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08810","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"UZTN6BEY25OC","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"pith_short_16","alias_value":"UZTN6BEY25OCRIWS","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"pith_short_8","alias_value":"UZTN6BEY","created_at":"2026-07-05T12:02:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UZTN6BEY25OCRIWSOZIEA33AWQ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.08810","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"62612d90e1848a00a9e5bc7aca9481cb1c7a8fea4df55cf3a648669bf326f77d","abstract_canon_sha256":"c2c2b9867696aa3abd989e3f82dc19a0f6c5b1a6deded065ea7f72a7927f57be"},"schema_version":"1.0"},"canonical_sha256":"a666df0498d75c28a2d27650406f60b40617ce41f5d58cfcd0f652c27fed035a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:47.006492Z","signature_b64":"kaoKcdVYAH9heobYLBIIPDed7inATqxjAPEn2cGkMcCOQLVj8qpYPjrz6LVC5aji9qMDsz/XjElNzrQkIPslAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a666df0498d75c28a2d27650406f60b40617ce41f5d58cfcd0f652c27fed035a","last_reissued_at":"2026-07-05T12:02:47.006017Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:47.006017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.08810","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:02:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrvFkbr8SFShpJhC/pZgtLSwpQvE22Nv8sI8Eo27nzqiqIJ2N+C8KpgF/CE5kY2zpFJZ/dxo1IlmXCUaSmdaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:40:28.530798Z"},"content_sha256":"505ee83cd9549da97e609010424000cfa1e04fe59b387dc998bc52d95ec6cb51","schema_version":"1.0","event_id":"sha256:505ee83cd9549da97e609010424000cfa1e04fe59b387dc998bc52d95ec6cb51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UZTN6BEY25OCRIWSOZIEA33AWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite induced-saturated graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Carla Groenland, Marthe Bonamy, Natasha Morrison, Tom Johnston","submitted_at":"2025-06-10T14:00:59Z","abstract_excerpt":"A graph $G$ is $H$-induced-saturated if $G$ is $H$-free but deleting any edge or adding any edge creates an induced copy of $H$. There are non-trivial graphs $H$, such as $P_4$, for which no finite $H$-induced-saturated graph $G$ exists. We show that for every finite graph $H$ that is not a clique or an independent set, there always exists a countable $H$-induced-saturated graph. In fact, we show that a far stronger property can be achieved: there is a countably infinite $H$-free graph $G$ such that any graph $G'\\ne G$ obtained by making a locally finite set of changes to $G$ contains a copy o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08810","kind":"arxiv","version":3},"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/2506.08810/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":"2026-07-05T12:02:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oZ9LmSHxUs4NYoONjyJHSzAgkiXMmRwfqyqzlnbt8rXCvcArRwtA1MlWbnuocHaE+g+53BwENkUm1ItacgrVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:40:28.531401Z"},"content_sha256":"3278a760f30391679677b40022cefa96aec5fcf0c7d0c22f2d87f34d6d53c8cd","schema_version":"1.0","event_id":"sha256:3278a760f30391679677b40022cefa96aec5fcf0c7d0c22f2d87f34d6d53c8cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZTN6BEY25OCRIWSOZIEA33AWQ/bundle.json","state_url":"https://pith.science/pith/UZTN6BEY25OCRIWSOZIEA33AWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZTN6BEY25OCRIWSOZIEA33AWQ/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":"2026-08-09T03:40:28Z","links":{"resolver":"https://pith.science/pith/UZTN6BEY25OCRIWSOZIEA33AWQ","bundle":"https://pith.science/pith/UZTN6BEY25OCRIWSOZIEA33AWQ/bundle.json","state":"https://pith.science/pith/UZTN6BEY25OCRIWSOZIEA33AWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZTN6BEY25OCRIWSOZIEA33AWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UZTN6BEY25OCRIWSOZIEA33AWQ","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":"c2c2b9867696aa3abd989e3f82dc19a0f6c5b1a6deded065ea7f72a7927f57be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:00:59Z","title_canon_sha256":"62612d90e1848a00a9e5bc7aca9481cb1c7a8fea4df55cf3a648669bf326f77d"},"schema_version":"1.0","source":{"id":"2506.08810","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08810","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08810v3","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08810","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"pith_short_12","alias_value":"UZTN6BEY25OC","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"pith_short_16","alias_value":"UZTN6BEY25OCRIWS","created_at":"2026-07-05T12:02:47Z"},{"alias_kind":"pith_short_8","alias_value":"UZTN6BEY","created_at":"2026-07-05T12:02:47Z"}],"graph_snapshots":[{"event_id":"sha256:3278a760f30391679677b40022cefa96aec5fcf0c7d0c22f2d87f34d6d53c8cd","target":"graph","created_at":"2026-07-05T12:02:47Z","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/2506.08810/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph $G$ is $H$-induced-saturated if $G$ is $H$-free but deleting any edge or adding any edge creates an induced copy of $H$. There are non-trivial graphs $H$, such as $P_4$, for which no finite $H$-induced-saturated graph $G$ exists. We show that for every finite graph $H$ that is not a clique or an independent set, there always exists a countable $H$-induced-saturated graph. In fact, we show that a far stronger property can be achieved: there is a countably infinite $H$-free graph $G$ such that any graph $G'\\ne G$ obtained by making a locally finite set of changes to $G$ contains a copy o","authors_text":"Alex Scott, Carla Groenland, Marthe Bonamy, Natasha Morrison, Tom Johnston","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:00:59Z","title":"Infinite induced-saturated graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08810","kind":"arxiv","version":3},"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":"sha256:505ee83cd9549da97e609010424000cfa1e04fe59b387dc998bc52d95ec6cb51","target":"record","created_at":"2026-07-05T12:02:47Z","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":"c2c2b9867696aa3abd989e3f82dc19a0f6c5b1a6deded065ea7f72a7927f57be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-10T14:00:59Z","title_canon_sha256":"62612d90e1848a00a9e5bc7aca9481cb1c7a8fea4df55cf3a648669bf326f77d"},"schema_version":"1.0","source":{"id":"2506.08810","kind":"arxiv","version":3}},"canonical_sha256":"a666df0498d75c28a2d27650406f60b40617ce41f5d58cfcd0f652c27fed035a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a666df0498d75c28a2d27650406f60b40617ce41f5d58cfcd0f652c27fed035a","first_computed_at":"2026-07-05T12:02:47.006017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:02:47.006017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kaoKcdVYAH9heobYLBIIPDed7inATqxjAPEn2cGkMcCOQLVj8qpYPjrz6LVC5aji9qMDsz/XjElNzrQkIPslAw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:02:47.006492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08810","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:505ee83cd9549da97e609010424000cfa1e04fe59b387dc998bc52d95ec6cb51","sha256:3278a760f30391679677b40022cefa96aec5fcf0c7d0c22f2d87f34d6d53c8cd"],"state_sha256":"49dd97f8385e3a1e29d9c2e8e2d294c59714aa154fc9e769114f51ac549854d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jX5i7b6lG0RQ4J7ayZ8Q7UfnPIOBIu2he3XG50vL5h0cbAb0Tf54zTnp+Ch/AeKay6vIRZh1ttzSy1SSnsqNCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:40:28.537049Z","bundle_sha256":"ba51781705474591d53cb39f8ee5edf830f8c1b588c14ddf2ff61f1414173d91"}}