{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:DTP5RBKFXNWJQSNL5ROMLP4LIK","short_pith_number":"pith:DTP5RBKF","schema_version":"1.0","canonical_sha256":"1cdfd88545bb6c9849abec5cc5bf8b429fcd806151974444f20e09a9d5eb3dc6","source":{"kind":"arxiv","id":"0707.0093","version":1},"attestation_state":"computed","paper":{"title":"Maximum overhang","license":"","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.HO","authors_text":"Mike Paterson, Mikkel Thorup, Peter Winkler, Uri Zwick, Yuval Peres","submitted_at":"2007-07-01T08:13:07Z","abstract_excerpt":"How far can a stack of $n$ identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order $\\log n$. Recently, Paterson and Zwick constructed $n$-block stacks with overhangs of order $n^{1/3}$, exponentially better than previously thought possible. We show here that order $n^{1/3}$ is indeed best possible, resolving the long-standing overhang problem up to a constant factor."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0707.0093","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.HO","submitted_at":"2007-07-01T08:13:07Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"5634763de4db0f4f971b00e53f6bfbc721d32e1ee7ea0006041d2e256aec1b74","abstract_canon_sha256":"19d918c7befa0a9e7bfb54d4104641a72d88bfb8d49c4a6455bdc0ccee7213be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:02:33.724703Z","signature_b64":"dHNve+cvQIDfhw3AIwYwIaOyLPVg1ibAzJL6CAwdWAp00B6nIMvoVB6nWz8PqfkjLlzrwMmHak9mZ2xr7rYdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cdfd88545bb6c9849abec5cc5bf8b429fcd806151974444f20e09a9d5eb3dc6","last_reissued_at":"2026-07-04T15:02:33.724309Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:02:33.724309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum overhang","license":"","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.HO","authors_text":"Mike Paterson, Mikkel Thorup, Peter Winkler, Uri Zwick, Yuval Peres","submitted_at":"2007-07-01T08:13:07Z","abstract_excerpt":"How far can a stack of $n$ identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order $\\log n$. Recently, Paterson and Zwick constructed $n$-block stacks with overhangs of order $n^{1/3}$, exponentially better than previously thought possible. We show here that order $n^{1/3}$ is indeed best possible, resolving the long-standing overhang problem up to a constant factor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0093","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/0707.0093/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0707.0093","created_at":"2026-07-04T15:02:33.724371+00:00"},{"alias_kind":"arxiv_version","alias_value":"0707.0093v1","created_at":"2026-07-04T15:02:33.724371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0093","created_at":"2026-07-04T15:02:33.724371+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTP5RBKFXNWJ","created_at":"2026-07-04T15:02:33.724371+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTP5RBKFXNWJQSNL","created_at":"2026-07-04T15:02:33.724371+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTP5RBKF","created_at":"2026-07-04T15:02:33.724371+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK","json":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK.json","graph_json":"https://pith.science/api/pith-number/DTP5RBKFXNWJQSNL5ROMLP4LIK/graph.json","events_json":"https://pith.science/api/pith-number/DTP5RBKFXNWJQSNL5ROMLP4LIK/events.json","paper":"https://pith.science/paper/DTP5RBKF"},"agent_actions":{"view_html":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK","download_json":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK.json","view_paper":"https://pith.science/paper/DTP5RBKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0707.0093&json=true","fetch_graph":"https://pith.science/api/pith-number/DTP5RBKFXNWJQSNL5ROMLP4LIK/graph.json","fetch_events":"https://pith.science/api/pith-number/DTP5RBKFXNWJQSNL5ROMLP4LIK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK/action/storage_attestation","attest_author":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK/action/author_attestation","sign_citation":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK/action/citation_signature","submit_replication":"https://pith.science/pith/DTP5RBKFXNWJQSNL5ROMLP4LIK/action/replication_record"}},"created_at":"2026-07-04T15:02:33.724371+00:00","updated_at":"2026-07-04T15:02:33.724371+00:00"}