{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JMDICY47SPST37QOKIK7S5HUBY","short_pith_number":"pith:JMDICY47","canonical_record":{"source":{"id":"1402.7105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T23:09:18Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4eb5dd97bd95e93b1f716775418ffcc07e3815c664bfa75ec2e48f0c390b6ff7","abstract_canon_sha256":"6264b4ee8be83447fd068351f33caafe5a2b1e0cde71eb37be0ad70b38971265"},"schema_version":"1.0"},"canonical_sha256":"4b0681639f93e53dfe0e5215f974f40e1c6933b7c20c8b30d7b62947048dec24","source":{"kind":"arxiv","id":"1402.7105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.7105","created_at":"2026-05-18T02:57:35Z"},{"alias_kind":"arxiv_version","alias_value":"1402.7105v1","created_at":"2026-05-18T02:57:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.7105","created_at":"2026-05-18T02:57:35Z"},{"alias_kind":"pith_short_12","alias_value":"JMDICY47SPST","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JMDICY47SPST37QO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JMDICY47","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JMDICY47SPST37QOKIK7S5HUBY","target":"record","payload":{"canonical_record":{"source":{"id":"1402.7105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T23:09:18Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4eb5dd97bd95e93b1f716775418ffcc07e3815c664bfa75ec2e48f0c390b6ff7","abstract_canon_sha256":"6264b4ee8be83447fd068351f33caafe5a2b1e0cde71eb37be0ad70b38971265"},"schema_version":"1.0"},"canonical_sha256":"4b0681639f93e53dfe0e5215f974f40e1c6933b7c20c8b30d7b62947048dec24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:35.036410Z","signature_b64":"y+qn2OtHcJWOiKs5TqWtWsrD544u58Td6BiGE9DjDsZxJs1MJD0azdtpU6KnWL5hFBp8KQzgu5xrlQIjkNmVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0681639f93e53dfe0e5215f974f40e1c6933b7c20c8b30d7b62947048dec24","last_reissued_at":"2026-05-18T02:57:35.035835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:35.035835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.7105","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":"2026-05-18T02:57:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m42Bsm6FD2nplESkL/q7P6+sK6H4XVg/Zjx65WWZJnKzqT6fYPV2hZOKJMdJZW43AQijrT5lxY3nxXfsqmAhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:44:16.239461Z"},"content_sha256":"2a54be36c0433b6041ff4d7d756806781e652004e3eb8719b5735e4006210da7","schema_version":"1.0","event_id":"sha256:2a54be36c0433b6041ff4d7d756806781e652004e3eb8719b5735e4006210da7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JMDICY47SPST37QOKIK7S5HUBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fool's Solitaire on Joins and Cartesian Products of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jennifer Wise, Sarah Loeb","submitted_at":"2014-02-27T23:09:18Z","abstract_excerpt":"Peg solitaire is a game generalized to connected graphs by Beeler and Hoilman. In the game pegs are placed on all but one vertex. If $xyz$ form a 3-vertex path and $x$ and $y$ each have a peg but $z$ does not, then we can remove the pegs at $x$ and $y$ and place a peg at $z$. By analogy with the moves in the original game, this is called a jump. The goal of the peg solitaire game on graphs is to find jumps that reduce the number of pegs on the graph to 1.\n  Beeler and Rodriguez proposed a variant where we instead want to maximize the number of pegs remaining when no more jumps can be made. Max"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7105","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":"2026-05-18T02:57:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xDZ9GdApPEcQzQ5Y5RHUgSGdoQRgs+pNcmCQfxI5o0figNJvAOsxDaz4OaZpMILV2MgJP4UqyRntmddJG9iqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:44:16.240099Z"},"content_sha256":"4a541d6bc4b0eb814fda67bf8162d42861191932956691474040dd7f28f15dda","schema_version":"1.0","event_id":"sha256:4a541d6bc4b0eb814fda67bf8162d42861191932956691474040dd7f28f15dda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMDICY47SPST37QOKIK7S5HUBY/bundle.json","state_url":"https://pith.science/pith/JMDICY47SPST37QOKIK7S5HUBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMDICY47SPST37QOKIK7S5HUBY/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":"2026-06-04T21:44:16Z","links":{"resolver":"https://pith.science/pith/JMDICY47SPST37QOKIK7S5HUBY","bundle":"https://pith.science/pith/JMDICY47SPST37QOKIK7S5HUBY/bundle.json","state":"https://pith.science/pith/JMDICY47SPST37QOKIK7S5HUBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMDICY47SPST37QOKIK7S5HUBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JMDICY47SPST37QOKIK7S5HUBY","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":"6264b4ee8be83447fd068351f33caafe5a2b1e0cde71eb37be0ad70b38971265","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T23:09:18Z","title_canon_sha256":"4eb5dd97bd95e93b1f716775418ffcc07e3815c664bfa75ec2e48f0c390b6ff7"},"schema_version":"1.0","source":{"id":"1402.7105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.7105","created_at":"2026-05-18T02:57:35Z"},{"alias_kind":"arxiv_version","alias_value":"1402.7105v1","created_at":"2026-05-18T02:57:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.7105","created_at":"2026-05-18T02:57:35Z"},{"alias_kind":"pith_short_12","alias_value":"JMDICY47SPST","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JMDICY47SPST37QO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JMDICY47","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:4a541d6bc4b0eb814fda67bf8162d42861191932956691474040dd7f28f15dda","target":"graph","created_at":"2026-05-18T02:57:35Z","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":"Peg solitaire is a game generalized to connected graphs by Beeler and Hoilman. In the game pegs are placed on all but one vertex. If $xyz$ form a 3-vertex path and $x$ and $y$ each have a peg but $z$ does not, then we can remove the pegs at $x$ and $y$ and place a peg at $z$. By analogy with the moves in the original game, this is called a jump. The goal of the peg solitaire game on graphs is to find jumps that reduce the number of pegs on the graph to 1.\n  Beeler and Rodriguez proposed a variant where we instead want to maximize the number of pegs remaining when no more jumps can be made. Max","authors_text":"Jennifer Wise, Sarah Loeb","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T23:09:18Z","title":"Fool's Solitaire on Joins and Cartesian Products of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7105","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":"sha256:2a54be36c0433b6041ff4d7d756806781e652004e3eb8719b5735e4006210da7","target":"record","created_at":"2026-05-18T02:57:35Z","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":"6264b4ee8be83447fd068351f33caafe5a2b1e0cde71eb37be0ad70b38971265","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T23:09:18Z","title_canon_sha256":"4eb5dd97bd95e93b1f716775418ffcc07e3815c664bfa75ec2e48f0c390b6ff7"},"schema_version":"1.0","source":{"id":"1402.7105","kind":"arxiv","version":1}},"canonical_sha256":"4b0681639f93e53dfe0e5215f974f40e1c6933b7c20c8b30d7b62947048dec24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0681639f93e53dfe0e5215f974f40e1c6933b7c20c8b30d7b62947048dec24","first_computed_at":"2026-05-18T02:57:35.035835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:35.035835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y+qn2OtHcJWOiKs5TqWtWsrD544u58Td6BiGE9DjDsZxJs1MJD0azdtpU6KnWL5hFBp8KQzgu5xrlQIjkNmVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:35.036410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.7105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a54be36c0433b6041ff4d7d756806781e652004e3eb8719b5735e4006210da7","sha256:4a541d6bc4b0eb814fda67bf8162d42861191932956691474040dd7f28f15dda"],"state_sha256":"d3b64b2d301ff9317ac0aac5ee030f077f347456620607d85da540f98e5414a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Qu7IUpbmT4mP6rMjU9kPX3GDlga4F6xMqle3TXWGoReq4PBm8MI7REFlmxCfAYDEFQmWSv6sU5LdTwaXedmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:44:16.243559Z","bundle_sha256":"e6863f1108b4ce26606f1ae68332a503b06b2ebdb4c473e4c984fce99ef114e1"}}