{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3FKTXYVNSA345XZDRU7DFBEUV2","short_pith_number":"pith:3FKTXYVN","canonical_record":{"source":{"id":"1708.04162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T14:57:30Z","cross_cats_sorted":[],"title_canon_sha256":"e3dc358a7bead4b8bfeccf297d7163a6f72bd1e676cb2456a24cc7613a502e15","abstract_canon_sha256":"1fc6a021508491034fc28d064dbdcb37752e25a51c8f5235a3748330c46b2582"},"schema_version":"1.0"},"canonical_sha256":"d9553be2ad9037cedf238d3e328494aeb86add71e31491b283bf41c6c69ae811","source":{"kind":"arxiv","id":"1708.04162","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04162","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04162v2","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04162","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"3FKTXYVNSA34","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3FKTXYVNSA345XZD","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3FKTXYVN","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3FKTXYVNSA345XZDRU7DFBEUV2","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T14:57:30Z","cross_cats_sorted":[],"title_canon_sha256":"e3dc358a7bead4b8bfeccf297d7163a6f72bd1e676cb2456a24cc7613a502e15","abstract_canon_sha256":"1fc6a021508491034fc28d064dbdcb37752e25a51c8f5235a3748330c46b2582"},"schema_version":"1.0"},"canonical_sha256":"d9553be2ad9037cedf238d3e328494aeb86add71e31491b283bf41c6c69ae811","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:57.272356Z","signature_b64":"2S0XQ1k47U49XwNFPfIGTDO6v54KfJegsVkhVXGpJ4w5PEGGXkm+XuDvGLwxZXPz8SH8uavW7E8EFo0Fu42UCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9553be2ad9037cedf238d3e328494aeb86add71e31491b283bf41c6c69ae811","last_reissued_at":"2026-05-18T00:37:57.271715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:57.271715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04162","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:37:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQzprsuOS9uxkXNvZkTLoWwtn2u7mHB2zhJVNcClq5szrHw0bIHXb/UUmjuvgA0qdoyOwgVmej1mnMSc0skhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:43.806524Z"},"content_sha256":"ebd2c05b0ff3aa91c2657077e3419fded56362bd2ed8bab4d04701aa525b83d3","schema_version":"1.0","event_id":"sha256:ebd2c05b0ff3aa91c2657077e3419fded56362bd2ed8bab4d04701aa525b83d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3FKTXYVNSA345XZDRU7DFBEUV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotically Almost Every $2r$-regular Graph has an Internal Partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Linial, Sria Louis","submitted_at":"2017-08-14T14:57:30Z","abstract_excerpt":"An internal partition of a graph is a partitioning of the vertex set into two parts such that for every vertex, at least half of its neighbors are on its side. We prove that for every positive integer $r$, asymptotically almost every $2r$-regular graph has an internal partition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04162","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:37:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpNqwl2IYsL29Sua1kX9duRfIOrg6zs8zFEEX3+/U3e5w0GGStcuMl6yvUfQGZmCf8CWnKoBLmvYQ+XwW2fJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:43.806872Z"},"content_sha256":"c1ba1939e2a638940d3c286b116dbfa276ae245f810f3af8db6fe61136f1502c","schema_version":"1.0","event_id":"sha256:c1ba1939e2a638940d3c286b116dbfa276ae245f810f3af8db6fe61136f1502c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FKTXYVNSA345XZDRU7DFBEUV2/bundle.json","state_url":"https://pith.science/pith/3FKTXYVNSA345XZDRU7DFBEUV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FKTXYVNSA345XZDRU7DFBEUV2/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":"2026-06-02T19:26:43Z","links":{"resolver":"https://pith.science/pith/3FKTXYVNSA345XZDRU7DFBEUV2","bundle":"https://pith.science/pith/3FKTXYVNSA345XZDRU7DFBEUV2/bundle.json","state":"https://pith.science/pith/3FKTXYVNSA345XZDRU7DFBEUV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FKTXYVNSA345XZDRU7DFBEUV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3FKTXYVNSA345XZDRU7DFBEUV2","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":"1fc6a021508491034fc28d064dbdcb37752e25a51c8f5235a3748330c46b2582","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T14:57:30Z","title_canon_sha256":"e3dc358a7bead4b8bfeccf297d7163a6f72bd1e676cb2456a24cc7613a502e15"},"schema_version":"1.0","source":{"id":"1708.04162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04162","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04162v2","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04162","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"3FKTXYVNSA34","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3FKTXYVNSA345XZD","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3FKTXYVN","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:c1ba1939e2a638940d3c286b116dbfa276ae245f810f3af8db6fe61136f1502c","target":"graph","created_at":"2026-05-18T00:37:57Z","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"},"paper":{"abstract_excerpt":"An internal partition of a graph is a partitioning of the vertex set into two parts such that for every vertex, at least half of its neighbors are on its side. We prove that for every positive integer $r$, asymptotically almost every $2r$-regular graph has an internal partition.","authors_text":"Nathan Linial, Sria Louis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T14:57:30Z","title":"Asymptotically Almost Every $2r$-regular Graph has an Internal Partition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04162","kind":"arxiv","version":2},"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:ebd2c05b0ff3aa91c2657077e3419fded56362bd2ed8bab4d04701aa525b83d3","target":"record","created_at":"2026-05-18T00:37:57Z","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":"1fc6a021508491034fc28d064dbdcb37752e25a51c8f5235a3748330c46b2582","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T14:57:30Z","title_canon_sha256":"e3dc358a7bead4b8bfeccf297d7163a6f72bd1e676cb2456a24cc7613a502e15"},"schema_version":"1.0","source":{"id":"1708.04162","kind":"arxiv","version":2}},"canonical_sha256":"d9553be2ad9037cedf238d3e328494aeb86add71e31491b283bf41c6c69ae811","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9553be2ad9037cedf238d3e328494aeb86add71e31491b283bf41c6c69ae811","first_computed_at":"2026-05-18T00:37:57.271715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:57.271715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2S0XQ1k47U49XwNFPfIGTDO6v54KfJegsVkhVXGpJ4w5PEGGXkm+XuDvGLwxZXPz8SH8uavW7E8EFo0Fu42UCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:57.272356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebd2c05b0ff3aa91c2657077e3419fded56362bd2ed8bab4d04701aa525b83d3","sha256:c1ba1939e2a638940d3c286b116dbfa276ae245f810f3af8db6fe61136f1502c"],"state_sha256":"dd7bc4290280c92bb1fe78ab10a8b7440a49691698f8229954ff30bcb5c9c30d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01mTfgBCTGKqwN2B1JyE2AhSypLDEOHzu5u4fLZW5zBE2Dw7707ySu4BIww+kdj1qVSAYuNT8o330wTCuKdZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:26:43.808866Z","bundle_sha256":"20145009f99be51bd665a4902234794c2d17ce50d975eb886f5f3f55e90281b6"}}