{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:MHXH43GTJN3POKNJ7DVW4274JD","short_pith_number":"pith:MHXH43GT","canonical_record":{"source":{"id":"math/0602498","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-02-22T14:01:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"def9710c214e9986eb31354f553f1f20b44a1fb65cd7c313ff7ad3b33e70859d","abstract_canon_sha256":"57a8c7919349feda857e53b2a3ee161dbc3efc1a5d8963047568f223e11004a1"},"schema_version":"1.0"},"canonical_sha256":"61ee7e6cd34b76f729a9f8eb6e6bfc48f4184e0945408ba087e8e89150340b8b","source":{"kind":"arxiv","id":"math/0602498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0602498","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"math/0602498v1","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602498","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"MHXH43GTJN3P","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MHXH43GTJN3POKNJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MHXH43GT","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:MHXH43GTJN3POKNJ7DVW4274JD","target":"record","payload":{"canonical_record":{"source":{"id":"math/0602498","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-02-22T14:01:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"def9710c214e9986eb31354f553f1f20b44a1fb65cd7c313ff7ad3b33e70859d","abstract_canon_sha256":"57a8c7919349feda857e53b2a3ee161dbc3efc1a5d8963047568f223e11004a1"},"schema_version":"1.0"},"canonical_sha256":"61ee7e6cd34b76f729a9f8eb6e6bfc48f4184e0945408ba087e8e89150340b8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:39.987548Z","signature_b64":"E6q7/NqG1y3+u5eIN0X5QWS3rQP95vN4lmdXByFz3H0bzFGS44ne7sqCZa5jdgNvk2/VEyX1i+gQoeuLeJfUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61ee7e6cd34b76f729a9f8eb6e6bfc48f4184e0945408ba087e8e89150340b8b","last_reissued_at":"2026-05-18T02:42:39.986753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:39.986753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0602498","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":"2026-05-18T02:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9mMj9fOGe6A79aBrLPx2WW3VsW56AupvA/0wCD/KRtHAYGmR7fm6H0yeycdxRAmTsB6TPM9IolwBMKcNbhNzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:07:43.832811Z"},"content_sha256":"8fe7318c1b621d401298d3c82e2734871eb7a83344d9f3dbd956e84de6b63c20","schema_version":"1.0","event_id":"sha256:8fe7318c1b621d401298d3c82e2734871eb7a83344d9f3dbd956e84de6b63c20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:MHXH43GTJN3POKNJ7DVW4274JD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Slow-Growing Sequence Defined by an Unusual Recurrence","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Allan R. Wilks, Dion C. Gijswijt, Fokko J. van de Bult, John P. Linderman, N. J. A. Sloane","submitted_at":"2006-02-22T14:01:22Z","abstract_excerpt":"The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY^k, where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the next term is k. The sequence begins 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, ... A 4 appears for the first time at position 220, but a 5 does not appear until about position 10^{10^{23}}. The main result of the paper is a proof that the sequence is unbounded. We also present results from extensive numerical investigations of the sequence and of certain derived sequences, culminating with a heuristic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602498","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":"2026-05-18T02:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43EKfb8NqC43d0/Cjh0Mgk8CbAAnH1q3BI18jRK/yxk+WvLS3B7w1oNH307tz8LsU2Lix0yMYlYX4qMGeQTKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:07:43.833502Z"},"content_sha256":"26e03c313c70e765edb2568b83b8b6fcbae66a0d2a971c6022193375830f155d","schema_version":"1.0","event_id":"sha256:26e03c313c70e765edb2568b83b8b6fcbae66a0d2a971c6022193375830f155d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHXH43GTJN3POKNJ7DVW4274JD/bundle.json","state_url":"https://pith.science/pith/MHXH43GTJN3POKNJ7DVW4274JD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHXH43GTJN3POKNJ7DVW4274JD/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":"2026-06-07T23:07:43Z","links":{"resolver":"https://pith.science/pith/MHXH43GTJN3POKNJ7DVW4274JD","bundle":"https://pith.science/pith/MHXH43GTJN3POKNJ7DVW4274JD/bundle.json","state":"https://pith.science/pith/MHXH43GTJN3POKNJ7DVW4274JD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHXH43GTJN3POKNJ7DVW4274JD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:MHXH43GTJN3POKNJ7DVW4274JD","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":"57a8c7919349feda857e53b2a3ee161dbc3efc1a5d8963047568f223e11004a1","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2006-02-22T14:01:22Z","title_canon_sha256":"def9710c214e9986eb31354f553f1f20b44a1fb65cd7c313ff7ad3b33e70859d"},"schema_version":"1.0","source":{"id":"math/0602498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0602498","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"math/0602498v1","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602498","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"MHXH43GTJN3P","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"MHXH43GTJN3POKNJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"MHXH43GT","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:26e03c313c70e765edb2568b83b8b6fcbae66a0d2a971c6022193375830f155d","target":"graph","created_at":"2026-05-18T02:42:39Z","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":"The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY^k, where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the next term is k. The sequence begins 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, ... A 4 appears for the first time at position 220, but a 5 does not appear until about position 10^{10^{23}}. The main result of the paper is a proof that the sequence is unbounded. We also present results from extensive numerical investigations of the sequence and of certain derived sequences, culminating with a heuristic ","authors_text":"Allan R. Wilks, Dion C. Gijswijt, Fokko J. van de Bult, John P. Linderman, N. J. A. Sloane","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-02-22T14:01:22Z","title":"A Slow-Growing Sequence Defined by an Unusual Recurrence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602498","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":"sha256:8fe7318c1b621d401298d3c82e2734871eb7a83344d9f3dbd956e84de6b63c20","target":"record","created_at":"2026-05-18T02:42:39Z","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":"57a8c7919349feda857e53b2a3ee161dbc3efc1a5d8963047568f223e11004a1","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2006-02-22T14:01:22Z","title_canon_sha256":"def9710c214e9986eb31354f553f1f20b44a1fb65cd7c313ff7ad3b33e70859d"},"schema_version":"1.0","source":{"id":"math/0602498","kind":"arxiv","version":1}},"canonical_sha256":"61ee7e6cd34b76f729a9f8eb6e6bfc48f4184e0945408ba087e8e89150340b8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ee7e6cd34b76f729a9f8eb6e6bfc48f4184e0945408ba087e8e89150340b8b","first_computed_at":"2026-05-18T02:42:39.986753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.986753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E6q7/NqG1y3+u5eIN0X5QWS3rQP95vN4lmdXByFz3H0bzFGS44ne7sqCZa5jdgNvk2/VEyX1i+gQoeuLeJfUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.987548Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0602498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fe7318c1b621d401298d3c82e2734871eb7a83344d9f3dbd956e84de6b63c20","sha256:26e03c313c70e765edb2568b83b8b6fcbae66a0d2a971c6022193375830f155d"],"state_sha256":"81a1a0c9c2ff0c00586d10fa07194a14c61fec8c50895ae618b266a1e1d80ab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyvln6yx2yggQ7MvgQCkR/KbatBSTOQB+2ArRsm+P3mnKIiXzceEZB6d5wqHdapu6VxA86MaFf6ygx8drU2BCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:07:43.837145Z","bundle_sha256":"11f6dd741ffad4c27954dc8f1709a7a41394ea2386e83869236d32e3d23f2d34"}}