{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:I57DUTODSJ3KXZATPHZSPTWTLM","short_pith_number":"pith:I57DUTOD","canonical_record":{"source":{"id":"2412.01937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2024-12-02T19:59:06Z","cross_cats_sorted":["cs.DM","cs.LG","cs.NE"],"title_canon_sha256":"ed4cccb57c1b923358ac314fc0e24be9c439989abb556a79205da06c68eed017","abstract_canon_sha256":"c13c4ad0fd35c055ed0e45d57ff348951c584a89744aabe80b7941ce0ce8ac65"},"schema_version":"1.0"},"canonical_sha256":"477e3a4dc39276abe41379f327ced35b14493e47551d66f21bc626228cf7d740","source":{"kind":"arxiv","id":"2412.01937","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01937","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01937v1","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01937","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"pith_short_12","alias_value":"I57DUTODSJ3K","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"pith_short_16","alias_value":"I57DUTODSJ3KXZAT","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"pith_short_8","alias_value":"I57DUTOD","created_at":"2026-07-05T09:43:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:I57DUTODSJ3KXZATPHZSPTWTLM","target":"record","payload":{"canonical_record":{"source":{"id":"2412.01937","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2024-12-02T19:59:06Z","cross_cats_sorted":["cs.DM","cs.LG","cs.NE"],"title_canon_sha256":"ed4cccb57c1b923358ac314fc0e24be9c439989abb556a79205da06c68eed017","abstract_canon_sha256":"c13c4ad0fd35c055ed0e45d57ff348951c584a89744aabe80b7941ce0ce8ac65"},"schema_version":"1.0"},"canonical_sha256":"477e3a4dc39276abe41379f327ced35b14493e47551d66f21bc626228cf7d740","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:43:41.274479Z","signature_b64":"sFgIkcLCZVsYXAG0pMMf7C9Fn5iIYJt/F/XjAxPRjbgXRASmIQzqGoLIvNCkc3LLKvs1cAAPNpIYQVRL4cSJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"477e3a4dc39276abe41379f327ced35b14493e47551d66f21bc626228cf7d740","last_reissued_at":"2026-07-05T09:43:41.273951Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:43:41.273951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.01937","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":"2026-07-05T09:43:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J8WdjxVlsVwf8wYmXCKWNJHtS6Qalcl/UizTNs+8yhvHdMCDUwZV2pzltJDEvvi1qZqYAJ4CivMl+bArhuKDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:45:09.197941Z"},"content_sha256":"f78b23348484ddb324331dab3a9c86ef467df3bfa5c9145d389a5868a9ad361a","schema_version":"1.0","event_id":"sha256:f78b23348484ddb324331dab3a9c86ef467df3bfa5c9145d389a5868a9ad361a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:I57DUTODSJ3KXZATPHZSPTWTLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximately Optimal Search on a Higher-dimensional Sliding Puzzle","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.LG","cs.NE"],"primary_cat":"cs.AI","authors_text":"\\'Erika Rold\\'an, Miguel O'Malley, Nono SC Merleau, Sayan Mukherjee","submitted_at":"2024-12-02T19:59:06Z","abstract_excerpt":"Higher-dimensional sliding puzzles are constructed on the vertices of a $d$-dimensional hypercube, where $2^d-l$ vertices are distinctly coloured. Rings with the same colours are initially set randomly on the vertices of the hypercube. The goal of the puzzle is to move each of the $2^d-l$ rings to pre-defined target vertices on the cube. In this setting, the $k$-rule constraint represents a generalisation of edge collision for the movement of colours between vertices, allowing movement only when a hypercube face of dimension $k$ containing a ring is completely free of other rings. Starting fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01937","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/2412.01937/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:43:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXMQMCAd5KgZfErRKRdeS1nlXswXOyJd/j04esA2GzEYuaPC+rBDEO5ehLfA4u3rksBnvWCW2agyO2wSoLO1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T15:45:09.198876Z"},"content_sha256":"28549af29026e40181173de4b311ae84d351983a81897d3b6f84971c612d7ebd","schema_version":"1.0","event_id":"sha256:28549af29026e40181173de4b311ae84d351983a81897d3b6f84971c612d7ebd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I57DUTODSJ3KXZATPHZSPTWTLM/bundle.json","state_url":"https://pith.science/pith/I57DUTODSJ3KXZATPHZSPTWTLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I57DUTODSJ3KXZATPHZSPTWTLM/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":"2026-08-12T15:45:09Z","links":{"resolver":"https://pith.science/pith/I57DUTODSJ3KXZATPHZSPTWTLM","bundle":"https://pith.science/pith/I57DUTODSJ3KXZATPHZSPTWTLM/bundle.json","state":"https://pith.science/pith/I57DUTODSJ3KXZATPHZSPTWTLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I57DUTODSJ3KXZATPHZSPTWTLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:I57DUTODSJ3KXZATPHZSPTWTLM","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":"c13c4ad0fd35c055ed0e45d57ff348951c584a89744aabe80b7941ce0ce8ac65","cross_cats_sorted":["cs.DM","cs.LG","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2024-12-02T19:59:06Z","title_canon_sha256":"ed4cccb57c1b923358ac314fc0e24be9c439989abb556a79205da06c68eed017"},"schema_version":"1.0","source":{"id":"2412.01937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01937","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01937v1","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01937","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"pith_short_12","alias_value":"I57DUTODSJ3K","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"pith_short_16","alias_value":"I57DUTODSJ3KXZAT","created_at":"2026-07-05T09:43:41Z"},{"alias_kind":"pith_short_8","alias_value":"I57DUTOD","created_at":"2026-07-05T09:43:41Z"}],"graph_snapshots":[{"event_id":"sha256:28549af29026e40181173de4b311ae84d351983a81897d3b6f84971c612d7ebd","target":"graph","created_at":"2026-07-05T09:43:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.01937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Higher-dimensional sliding puzzles are constructed on the vertices of a $d$-dimensional hypercube, where $2^d-l$ vertices are distinctly coloured. Rings with the same colours are initially set randomly on the vertices of the hypercube. The goal of the puzzle is to move each of the $2^d-l$ rings to pre-defined target vertices on the cube. In this setting, the $k$-rule constraint represents a generalisation of edge collision for the movement of colours between vertices, allowing movement only when a hypercube face of dimension $k$ containing a ring is completely free of other rings. Starting fro","authors_text":"\\'Erika Rold\\'an, Miguel O'Malley, Nono SC Merleau, Sayan Mukherjee","cross_cats":["cs.DM","cs.LG","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2024-12-02T19:59:06Z","title":"Approximately Optimal Search on a Higher-dimensional Sliding Puzzle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01937","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:f78b23348484ddb324331dab3a9c86ef467df3bfa5c9145d389a5868a9ad361a","target":"record","created_at":"2026-07-05T09:43:41Z","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":"c13c4ad0fd35c055ed0e45d57ff348951c584a89744aabe80b7941ce0ce8ac65","cross_cats_sorted":["cs.DM","cs.LG","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2024-12-02T19:59:06Z","title_canon_sha256":"ed4cccb57c1b923358ac314fc0e24be9c439989abb556a79205da06c68eed017"},"schema_version":"1.0","source":{"id":"2412.01937","kind":"arxiv","version":1}},"canonical_sha256":"477e3a4dc39276abe41379f327ced35b14493e47551d66f21bc626228cf7d740","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"477e3a4dc39276abe41379f327ced35b14493e47551d66f21bc626228cf7d740","first_computed_at":"2026-07-05T09:43:41.273951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:43:41.273951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sFgIkcLCZVsYXAG0pMMf7C9Fn5iIYJt/F/XjAxPRjbgXRASmIQzqGoLIvNCkc3LLKvs1cAAPNpIYQVRL4cSJCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:43:41.274479Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.01937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78b23348484ddb324331dab3a9c86ef467df3bfa5c9145d389a5868a9ad361a","sha256:28549af29026e40181173de4b311ae84d351983a81897d3b6f84971c612d7ebd"],"state_sha256":"0da419d7e87196712d61e0368ea0bcc979921b152d3d9b94c971de478304e1f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"effYEUWeWupHmRgHYY+MHMSM1tdk2Em5FR5RbHwoMtLMFQNfYYsWSKFF8L+FcI1kDq7cnGgl2HekFPS39h80AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T15:45:09.204824Z","bundle_sha256":"c2aa3cf9f09699a1f5d9758881c55a56fdaa690a3a2f58b267ccdc9e4dca9d78"}}