{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:53LJDECR33QTTBMQH3XMFAZXIP","short_pith_number":"pith:53LJDECR","canonical_record":{"source":{"id":"1311.4109","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-17T02:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"aa5af9a4dab1e9a3ac3c092efe46926d20b73dcc253aae271c1ee5dd2251bf4d","abstract_canon_sha256":"8dddde2e2ddaa5a3b68cb4b72d18c42bdd7bee63924b08a0b7044108b600ec4d"},"schema_version":"1.0"},"canonical_sha256":"eed6919051dee13985903eeec2833743d3db5c9d33d6c20e79267aa315b7537e","source":{"kind":"arxiv","id":"1311.4109","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4109","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4109v3","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4109","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"53LJDECR33QT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"53LJDECR33QTTBMQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"53LJDECR","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:53LJDECR33QTTBMQH3XMFAZXIP","target":"record","payload":{"canonical_record":{"source":{"id":"1311.4109","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-17T02:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"aa5af9a4dab1e9a3ac3c092efe46926d20b73dcc253aae271c1ee5dd2251bf4d","abstract_canon_sha256":"8dddde2e2ddaa5a3b68cb4b72d18c42bdd7bee63924b08a0b7044108b600ec4d"},"schema_version":"1.0"},"canonical_sha256":"eed6919051dee13985903eeec2833743d3db5c9d33d6c20e79267aa315b7537e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:16.355594Z","signature_b64":"j7SgkRyfsFf3G3iKux60wRwAgSoMheTtE11kqjm0o7lgTH5gxvFFLtL1ClMUtC0o4jwP4TInEOu8vTt+t7/oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eed6919051dee13985903eeec2833743d3db5c9d33d6c20e79267aa315b7537e","last_reissued_at":"2026-05-18T01:01:16.355086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:16.355086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.4109","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":"2026-05-18T01:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FYi1iAuknTFMW3u/sQxSu2WgAMLny+2sqUo7G2uKCJegjygEm4NQ0RA0z9m0/TZd0x11GgvOfzABlibi+yQPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:16:19.575909Z"},"content_sha256":"3094a0acbacbe51c00d0e72a967610f8c44d182dedafb68219f538460380a43c","schema_version":"1.0","event_id":"sha256:3094a0acbacbe51c00d0e72a967610f8c44d182dedafb68219f538460380a43c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:53LJDECR33QTTBMQH3XMFAZXIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised Knight's Tours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nina Kam\\v{c}ev","submitted_at":"2013-11-17T02:18:17Z","abstract_excerpt":"The problem of existence of closed knight's tours in $[n]^d$, where $[n]=\\{0, 1, \\dots, n-1\\}$, was recently solved by Erde, Gol\\'{e}nia, and Gol\\'{e}nia. They raised the same question for a generalised, $(a, b)$ knight, which is allowed to move along any two axes of $[n]^d$ by $a$ and $b$ unit lengths respectively. Given an even number $a$, we show that the $[n]^d$ grid admits an $(a, 1)$ knight's tour for sufficiently large even side length $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4109","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":""},"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":"2026-05-18T01:01:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfyw5Jy0vKPNbgZcKbsAO7pJeo6xiUCOC63RXMm/UnfMyn6eH+acxuQ/8J32Ysy0fYBujBKnhQbp5WrAvqY0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:16:19.576257Z"},"content_sha256":"170d7c3ee467e084d2892dd8922b3339368378c8722855b77cba0626ccd52f1b","schema_version":"1.0","event_id":"sha256:170d7c3ee467e084d2892dd8922b3339368378c8722855b77cba0626ccd52f1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53LJDECR33QTTBMQH3XMFAZXIP/bundle.json","state_url":"https://pith.science/pith/53LJDECR33QTTBMQH3XMFAZXIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53LJDECR33QTTBMQH3XMFAZXIP/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":"2026-07-04T18:16:19Z","links":{"resolver":"https://pith.science/pith/53LJDECR33QTTBMQH3XMFAZXIP","bundle":"https://pith.science/pith/53LJDECR33QTTBMQH3XMFAZXIP/bundle.json","state":"https://pith.science/pith/53LJDECR33QTTBMQH3XMFAZXIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53LJDECR33QTTBMQH3XMFAZXIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:53LJDECR33QTTBMQH3XMFAZXIP","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":"8dddde2e2ddaa5a3b68cb4b72d18c42bdd7bee63924b08a0b7044108b600ec4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-17T02:18:17Z","title_canon_sha256":"aa5af9a4dab1e9a3ac3c092efe46926d20b73dcc253aae271c1ee5dd2251bf4d"},"schema_version":"1.0","source":{"id":"1311.4109","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4109","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4109v3","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4109","created_at":"2026-05-18T01:01:16Z"},{"alias_kind":"pith_short_12","alias_value":"53LJDECR33QT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"53LJDECR33QTTBMQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"53LJDECR","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:170d7c3ee467e084d2892dd8922b3339368378c8722855b77cba0626ccd52f1b","target":"graph","created_at":"2026-05-18T01:01:16Z","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 problem of existence of closed knight's tours in $[n]^d$, where $[n]=\\{0, 1, \\dots, n-1\\}$, was recently solved by Erde, Gol\\'{e}nia, and Gol\\'{e}nia. They raised the same question for a generalised, $(a, b)$ knight, which is allowed to move along any two axes of $[n]^d$ by $a$ and $b$ unit lengths respectively. Given an even number $a$, we show that the $[n]^d$ grid admits an $(a, 1)$ knight's tour for sufficiently large even side length $n$.","authors_text":"Nina Kam\\v{c}ev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-17T02:18:17Z","title":"Generalised Knight's Tours"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4109","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":"sha256:3094a0acbacbe51c00d0e72a967610f8c44d182dedafb68219f538460380a43c","target":"record","created_at":"2026-05-18T01:01:16Z","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":"8dddde2e2ddaa5a3b68cb4b72d18c42bdd7bee63924b08a0b7044108b600ec4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-17T02:18:17Z","title_canon_sha256":"aa5af9a4dab1e9a3ac3c092efe46926d20b73dcc253aae271c1ee5dd2251bf4d"},"schema_version":"1.0","source":{"id":"1311.4109","kind":"arxiv","version":3}},"canonical_sha256":"eed6919051dee13985903eeec2833743d3db5c9d33d6c20e79267aa315b7537e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eed6919051dee13985903eeec2833743d3db5c9d33d6c20e79267aa315b7537e","first_computed_at":"2026-05-18T01:01:16.355086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:16.355086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j7SgkRyfsFf3G3iKux60wRwAgSoMheTtE11kqjm0o7lgTH5gxvFFLtL1ClMUtC0o4jwP4TInEOu8vTt+t7/oDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:16.355594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4109","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3094a0acbacbe51c00d0e72a967610f8c44d182dedafb68219f538460380a43c","sha256:170d7c3ee467e084d2892dd8922b3339368378c8722855b77cba0626ccd52f1b"],"state_sha256":"48189156fcfb230309cbea86fa68b4d0c169c257af1cc462c4f7216260264943"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JeCyUZi7qHTxVNKH9Z+L5RXDJLsI9Uya56BprwNSwmIdsEHjUjKmeUa75XgWvoqeTnM3xXZJ4kSECNr1xL4ICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:16:19.578238Z","bundle_sha256":"9bd9d65b0fa560877cc72ac35a0a6aa065f8732c0957003172d09eec8f36e78f"}}