{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VAC2FQ5O42VZSGMEYY4TDDQGZ7","short_pith_number":"pith:VAC2FQ5O","canonical_record":{"source":{"id":"1009.5731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T01:36:20Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"4de581ab9232c86ec19a108032ef5815b8441b37922a73fbda6e7b0e7059f9ae","abstract_canon_sha256":"4231c84a146f22026e3a67049ac398d317c851390ba971518a704307b9e003e9"},"schema_version":"1.0"},"canonical_sha256":"a805a2c3aee6ab991984c639318e06cfe82de0e3035ac586f86651e47b46f58b","source":{"kind":"arxiv","id":"1009.5731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5731","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5731v1","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5731","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"VAC2FQ5O42VZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VAC2FQ5O42VZSGME","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VAC2FQ5O","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VAC2FQ5O42VZSGMEYY4TDDQGZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T01:36:20Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"4de581ab9232c86ec19a108032ef5815b8441b37922a73fbda6e7b0e7059f9ae","abstract_canon_sha256":"4231c84a146f22026e3a67049ac398d317c851390ba971518a704307b9e003e9"},"schema_version":"1.0"},"canonical_sha256":"a805a2c3aee6ab991984c639318e06cfe82de0e3035ac586f86651e47b46f58b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:09.064422Z","signature_b64":"Pby+aObycRv5imqMY86MIuLdHQx8JWpT+Bd+yHl8aMN/qzlrrZ9qzjZTBoNljvolj3oh8V0BcHkchDBtAZpcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a805a2c3aee6ab991984c639318e06cfe82de0e3035ac586f86651e47b46f58b","last_reissued_at":"2026-05-18T04:40:09.063909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:09.063909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5731","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qGD+r3AyfdoOrVLFUvS81uJtUcCR7JpGCgQs9zyF99wugcfuhzkSqcmd6tOj0y13C9uDhtk8KJwoAhblPEiEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:15:04.810168Z"},"content_sha256":"ca86a2c784180f92caffecdfcf7e66de5d509955387fc963579b8115a894bf2d","schema_version":"1.0","event_id":"sha256:ca86a2c784180f92caffecdfcf7e66de5d509955387fc963579b8115a894bf2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VAC2FQ5O42VZSGMEYY4TDDQGZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Explicit Solution to the Chessboard Pebbling Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Charles Knessl, Qiang Zhen","submitted_at":"2010-09-29T01:36:20Z","abstract_excerpt":"We consider the chessboard pebbling problem analyzed by Chung, Graham, Morrison and Odlyzko [3]. We study the number of reachable configurations $G(k)$ and a related double sequence $G(k,m)$. Exact expressions for these are derived, and we then consider various asymptotic limits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5731","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMKT7/kL/2cyj5YiEixDUCn9ekop+dke4L2+u9YLU1C2gaBcMDeoZ41kD6vBkPF+zWaxFE+slfAd7NJqKNJ2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:15:04.810550Z"},"content_sha256":"61aa5e9b386528625a00d10783df41002eccbba063aff8af0e022991a580cdae","schema_version":"1.0","event_id":"sha256:61aa5e9b386528625a00d10783df41002eccbba063aff8af0e022991a580cdae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7/bundle.json","state_url":"https://pith.science/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7/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":"2026-05-30T11:15:04Z","links":{"resolver":"https://pith.science/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7","bundle":"https://pith.science/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7/bundle.json","state":"https://pith.science/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VAC2FQ5O42VZSGMEYY4TDDQGZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VAC2FQ5O42VZSGMEYY4TDDQGZ7","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":"4231c84a146f22026e3a67049ac398d317c851390ba971518a704307b9e003e9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T01:36:20Z","title_canon_sha256":"4de581ab9232c86ec19a108032ef5815b8441b37922a73fbda6e7b0e7059f9ae"},"schema_version":"1.0","source":{"id":"1009.5731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5731","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5731v1","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5731","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"VAC2FQ5O42VZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VAC2FQ5O42VZSGME","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VAC2FQ5O","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:61aa5e9b386528625a00d10783df41002eccbba063aff8af0e022991a580cdae","target":"graph","created_at":"2026-05-18T04:40:09Z","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":"We consider the chessboard pebbling problem analyzed by Chung, Graham, Morrison and Odlyzko [3]. We study the number of reachable configurations $G(k)$ and a related double sequence $G(k,m)$. Exact expressions for these are derived, and we then consider various asymptotic limits.","authors_text":"Charles Knessl, Qiang Zhen","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T01:36:20Z","title":"An Explicit Solution to the Chessboard Pebbling Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5731","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:ca86a2c784180f92caffecdfcf7e66de5d509955387fc963579b8115a894bf2d","target":"record","created_at":"2026-05-18T04:40:09Z","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":"4231c84a146f22026e3a67049ac398d317c851390ba971518a704307b9e003e9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T01:36:20Z","title_canon_sha256":"4de581ab9232c86ec19a108032ef5815b8441b37922a73fbda6e7b0e7059f9ae"},"schema_version":"1.0","source":{"id":"1009.5731","kind":"arxiv","version":1}},"canonical_sha256":"a805a2c3aee6ab991984c639318e06cfe82de0e3035ac586f86651e47b46f58b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a805a2c3aee6ab991984c639318e06cfe82de0e3035ac586f86651e47b46f58b","first_computed_at":"2026-05-18T04:40:09.063909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.063909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pby+aObycRv5imqMY86MIuLdHQx8JWpT+Bd+yHl8aMN/qzlrrZ9qzjZTBoNljvolj3oh8V0BcHkchDBtAZpcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.064422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca86a2c784180f92caffecdfcf7e66de5d509955387fc963579b8115a894bf2d","sha256:61aa5e9b386528625a00d10783df41002eccbba063aff8af0e022991a580cdae"],"state_sha256":"13dbe33ee49d264195b44ea7eb27b6a10fc7631a45f42d5a533f78695fe4f4da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/TnlVwk3bD6/SuYj4D9gCKcdgvm/9d0B+6YmQBDAqCmEQe9hYLhVGw100HZ0zKFY8vVa2TSDpV7aMrp7dWSAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:15:04.812591Z","bundle_sha256":"ac69b2494c505770523bf0e7c9bbf9c7f3ac765b5214e92b604dc03fa71c2b99"}}