{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:D2P4K55INHKUEF6XY7Z7BW6DDB","short_pith_number":"pith:D2P4K55I","canonical_record":{"source":{"id":"1604.04338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-15T02:33:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"c299e499e51ec6e530195256b0e00e45c7242fa8fb8d8f88eb9b61d10c3da2c8","abstract_canon_sha256":"0b9f3ee84b9cce0fd4c837cd581f7b7bde1bfe4d09d8835a5e4b57a6e878004a"},"schema_version":"1.0"},"canonical_sha256":"1e9fc577a869d54217d7c7f3f0dbc3187134339e3d3abc8d4e43346e3fad8de4","source":{"kind":"arxiv","id":"1604.04338","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04338","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04338v1","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04338","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"D2P4K55INHKU","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D2P4K55INHKUEF6X","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D2P4K55I","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:D2P4K55INHKUEF6XY7Z7BW6DDB","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-15T02:33:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"c299e499e51ec6e530195256b0e00e45c7242fa8fb8d8f88eb9b61d10c3da2c8","abstract_canon_sha256":"0b9f3ee84b9cce0fd4c837cd581f7b7bde1bfe4d09d8835a5e4b57a6e878004a"},"schema_version":"1.0"},"canonical_sha256":"1e9fc577a869d54217d7c7f3f0dbc3187134339e3d3abc8d4e43346e3fad8de4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:04.456286Z","signature_b64":"dLkYPci8wb2enrsJ1LgBnBBHH+tO7IH5aL25jZ84LrPl1d8yULmJJpAIrcyb1PqR+SGv13mYTVr6mJsU+AtBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e9fc577a869d54217d7c7f3f0dbc3187134339e3d3abc8d4e43346e3fad8de4","last_reissued_at":"2026-05-18T01:17:04.455585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:04.455585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04338","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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGG9snp14E+T3SsyVA+9n32aEEtlrXQ5rfiNa0z2+i/lEFXtek0Bf0iJ9h30ymBQ37eoGjZBvDgYx6kRDp8OBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:37:23.514102Z"},"content_sha256":"1843522f0efea2348c73845a4061a3596bc97c3bc82a8908157e64278585ee4a","schema_version":"1.0","event_id":"sha256:1843522f0efea2348c73845a4061a3596bc97c3bc82a8908157e64278585ee4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:D2P4K55INHKUEF6XY7Z7BW6DDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple proof of tail--polynomial bounds on the diameter of polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OC","authors_text":"Noriyoshi Sukegawa, Shinji Mizuno","submitted_at":"2016-04-15T02:33:17Z","abstract_excerpt":"Let $\\Delta(d,n)$ denote the maximum diameter of a $d$-dimensional polyhedron with $n$ facets. In this paper, we propose a unified analysis of a recursive inequality about $\\Delta(d,n)$ established by Kalai and Kleitman in 1992. This yields much simpler proofs of a tail--polynomial and tail--almost--linear bounds on $\\Delta(d,n)$ which are recently discussed by Gallagher and Kim."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04338","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":""},"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":"2026-05-18T01:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wjv2TznlhLmFVegYBIbDh1oHfxY15wWdn9Om0gl7RzfXPRIZm+73cbIcIrDY6bBvYHALgf9dsPzvBo6zNqGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:37:23.514459Z"},"content_sha256":"8fd2e8b2db9e0a84b81d3ae191a9c5f87b66da01e02ff68e85baa7d260b7b929","schema_version":"1.0","event_id":"sha256:8fd2e8b2db9e0a84b81d3ae191a9c5f87b66da01e02ff68e85baa7d260b7b929"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2P4K55INHKUEF6XY7Z7BW6DDB/bundle.json","state_url":"https://pith.science/pith/D2P4K55INHKUEF6XY7Z7BW6DDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2P4K55INHKUEF6XY7Z7BW6DDB/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":"2026-06-26T01:37:23Z","links":{"resolver":"https://pith.science/pith/D2P4K55INHKUEF6XY7Z7BW6DDB","bundle":"https://pith.science/pith/D2P4K55INHKUEF6XY7Z7BW6DDB/bundle.json","state":"https://pith.science/pith/D2P4K55INHKUEF6XY7Z7BW6DDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2P4K55INHKUEF6XY7Z7BW6DDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D2P4K55INHKUEF6XY7Z7BW6DDB","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":"0b9f3ee84b9cce0fd4c837cd581f7b7bde1bfe4d09d8835a5e4b57a6e878004a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-15T02:33:17Z","title_canon_sha256":"c299e499e51ec6e530195256b0e00e45c7242fa8fb8d8f88eb9b61d10c3da2c8"},"schema_version":"1.0","source":{"id":"1604.04338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04338","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04338v1","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04338","created_at":"2026-05-18T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"D2P4K55INHKU","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D2P4K55INHKUEF6X","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D2P4K55I","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:8fd2e8b2db9e0a84b81d3ae191a9c5f87b66da01e02ff68e85baa7d260b7b929","target":"graph","created_at":"2026-05-18T01:17:04Z","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":"Let $\\Delta(d,n)$ denote the maximum diameter of a $d$-dimensional polyhedron with $n$ facets. In this paper, we propose a unified analysis of a recursive inequality about $\\Delta(d,n)$ established by Kalai and Kleitman in 1992. This yields much simpler proofs of a tail--polynomial and tail--almost--linear bounds on $\\Delta(d,n)$ which are recently discussed by Gallagher and Kim.","authors_text":"Noriyoshi Sukegawa, Shinji Mizuno","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-15T02:33:17Z","title":"A simple proof of tail--polynomial bounds on the diameter of polyhedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04338","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":"sha256:1843522f0efea2348c73845a4061a3596bc97c3bc82a8908157e64278585ee4a","target":"record","created_at":"2026-05-18T01:17:04Z","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":"0b9f3ee84b9cce0fd4c837cd581f7b7bde1bfe4d09d8835a5e4b57a6e878004a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-15T02:33:17Z","title_canon_sha256":"c299e499e51ec6e530195256b0e00e45c7242fa8fb8d8f88eb9b61d10c3da2c8"},"schema_version":"1.0","source":{"id":"1604.04338","kind":"arxiv","version":1}},"canonical_sha256":"1e9fc577a869d54217d7c7f3f0dbc3187134339e3d3abc8d4e43346e3fad8de4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e9fc577a869d54217d7c7f3f0dbc3187134339e3d3abc8d4e43346e3fad8de4","first_computed_at":"2026-05-18T01:17:04.455585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:04.455585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLkYPci8wb2enrsJ1LgBnBBHH+tO7IH5aL25jZ84LrPl1d8yULmJJpAIrcyb1PqR+SGv13mYTVr6mJsU+AtBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:04.456286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1843522f0efea2348c73845a4061a3596bc97c3bc82a8908157e64278585ee4a","sha256:8fd2e8b2db9e0a84b81d3ae191a9c5f87b66da01e02ff68e85baa7d260b7b929"],"state_sha256":"6800f8417ef374b27c69912b4ecaf626c306b0abcb72add24f01c51af72e1bc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q8U7O6xrwHSp9xoeHfIwstKHGjLYLKJmqeNVr4Fgh+IEVjEn1RYu/qeAkpb75J+0ln9KHP5G1ANO2orDaolnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:37:23.516419Z","bundle_sha256":"291db8494218dfebb4c94668043487ec5bd12f47ebfeac59d24f24f85b316b20"}}