{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MRRTD5IWANXGCZRNLBDTVE4HZW","short_pith_number":"pith:MRRTD5IW","canonical_record":{"source":{"id":"1308.0892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-08-05T05:51:35Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"1fe1daf1773870e8658be53eff6e8c8d757c3722ecb0b4da80b813bad7a0f27b","abstract_canon_sha256":"ad2f7f63424971350788fd9498846b9481b99fb57044b211de6bc552c494ed56"},"schema_version":"1.0"},"canonical_sha256":"646331f516036e61662d58473a9387cd93a56bb4f380593eea07c127f8991898","source":{"kind":"arxiv","id":"1308.0892","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0892","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0892v2","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0892","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"MRRTD5IWANXG","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MRRTD5IWANXGCZRN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MRRTD5IW","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MRRTD5IWANXGCZRNLBDTVE4HZW","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-08-05T05:51:35Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"1fe1daf1773870e8658be53eff6e8c8d757c3722ecb0b4da80b813bad7a0f27b","abstract_canon_sha256":"ad2f7f63424971350788fd9498846b9481b99fb57044b211de6bc552c494ed56"},"schema_version":"1.0"},"canonical_sha256":"646331f516036e61662d58473a9387cd93a56bb4f380593eea07c127f8991898","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:10.342521Z","signature_b64":"g+vliRQjGXky8fh6raSDXN+t928GHzYur6t58sxn+MD2Aw5RWOhS+SgjGs28LnDJsSCodwialr2XoZste3juAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"646331f516036e61662d58473a9387cd93a56bb4f380593eea07c127f8991898","last_reissued_at":"2026-05-18T00:27:10.341974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:10.341974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0892","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/vt6WK57MpL0Zi1FXPAruWHH0ArCHQv7bIsgy+VXBPrG0/0G2SkjLa47Sk9cKlGSwxKk0FKJuZ6CckNc4HLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:21:25.525784Z"},"content_sha256":"9b2e853d0d42d562197291c61ce07c71708a3bab38862485e76b98b17d1d4e4a","schema_version":"1.0","event_id":"sha256:9b2e853d0d42d562197291c61ce07c71708a3bab38862485e76b98b17d1d4e4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MRRTD5IWANXGCZRNLBDTVE4HZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alcuin's Propositiones de Civitatibus: the Earliest Packing Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.HO","authors_text":"Nikolai Yu. Zolotykh","submitted_at":"2013-08-05T05:51:35Z","abstract_excerpt":"We consider three problems about cities from Alcuin's_Propositiones ad acuendos juvenes_. These problems can be considered as the earliest packing problems difficult also for modern state-of-the-art packing algorithms. We discuss the Alcuin's solutions and give the known (to the author) best solutions to these problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0892","kind":"arxiv","version":2},"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":"2026-05-18T00:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4+u6OBGeXVD71O4JJF9Jvg7DwnlBUqVa32+AlGkXTh9UWLDagJpG1/ueI9KIGfYBFAXniNoAkBYul22NiMXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:21:25.526476Z"},"content_sha256":"14d1370ce04878de9e853a79f8808fa729d1eb663b64e5faa63056bbbad709cc","schema_version":"1.0","event_id":"sha256:14d1370ce04878de9e853a79f8808fa729d1eb663b64e5faa63056bbbad709cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRRTD5IWANXGCZRNLBDTVE4HZW/bundle.json","state_url":"https://pith.science/pith/MRRTD5IWANXGCZRNLBDTVE4HZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRRTD5IWANXGCZRNLBDTVE4HZW/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":"2026-06-07T23:21:25Z","links":{"resolver":"https://pith.science/pith/MRRTD5IWANXGCZRNLBDTVE4HZW","bundle":"https://pith.science/pith/MRRTD5IWANXGCZRNLBDTVE4HZW/bundle.json","state":"https://pith.science/pith/MRRTD5IWANXGCZRNLBDTVE4HZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRRTD5IWANXGCZRNLBDTVE4HZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MRRTD5IWANXGCZRNLBDTVE4HZW","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":"ad2f7f63424971350788fd9498846b9481b99fb57044b211de6bc552c494ed56","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-08-05T05:51:35Z","title_canon_sha256":"1fe1daf1773870e8658be53eff6e8c8d757c3722ecb0b4da80b813bad7a0f27b"},"schema_version":"1.0","source":{"id":"1308.0892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0892","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0892v2","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0892","created_at":"2026-05-18T00:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"MRRTD5IWANXG","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MRRTD5IWANXGCZRN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MRRTD5IW","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:14d1370ce04878de9e853a79f8808fa729d1eb663b64e5faa63056bbbad709cc","target":"graph","created_at":"2026-05-18T00:27:10Z","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 three problems about cities from Alcuin's_Propositiones ad acuendos juvenes_. These problems can be considered as the earliest packing problems difficult also for modern state-of-the-art packing algorithms. We discuss the Alcuin's solutions and give the known (to the author) best solutions to these problems.","authors_text":"Nikolai Yu. Zolotykh","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-08-05T05:51:35Z","title":"Alcuin's Propositiones de Civitatibus: the Earliest Packing Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0892","kind":"arxiv","version":2},"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":"sha256:9b2e853d0d42d562197291c61ce07c71708a3bab38862485e76b98b17d1d4e4a","target":"record","created_at":"2026-05-18T00:27:10Z","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":"ad2f7f63424971350788fd9498846b9481b99fb57044b211de6bc552c494ed56","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-08-05T05:51:35Z","title_canon_sha256":"1fe1daf1773870e8658be53eff6e8c8d757c3722ecb0b4da80b813bad7a0f27b"},"schema_version":"1.0","source":{"id":"1308.0892","kind":"arxiv","version":2}},"canonical_sha256":"646331f516036e61662d58473a9387cd93a56bb4f380593eea07c127f8991898","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"646331f516036e61662d58473a9387cd93a56bb4f380593eea07c127f8991898","first_computed_at":"2026-05-18T00:27:10.341974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:10.341974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g+vliRQjGXky8fh6raSDXN+t928GHzYur6t58sxn+MD2Aw5RWOhS+SgjGs28LnDJsSCodwialr2XoZste3juAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:10.342521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b2e853d0d42d562197291c61ce07c71708a3bab38862485e76b98b17d1d4e4a","sha256:14d1370ce04878de9e853a79f8808fa729d1eb663b64e5faa63056bbbad709cc"],"state_sha256":"3194c57d561bdf7665cb9575e66664083455e21e0078a418220b8c2b61eb0b70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BxlDRNDlpzrMYgDUpM9uYUN/LRG+hzHfHRZg1LjEwCb9T/k4z+2daXe7NvfKLF50xsRvh7xoyOCXWWRYZDLFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:21:25.530551Z","bundle_sha256":"a17184e2d25fa967fb030bcbd321b023633a29db002523c1f347ea294c5557e9"}}