{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B2SUY52PDFOASBPDKMCKKHHOCT","short_pith_number":"pith:B2SUY52P","canonical_record":{"source":{"id":"1206.0152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-01T11:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"f025a0795c20552883cd3785231412639a250caab8ab5f3753b96f8e1f312809","abstract_canon_sha256":"ba123cac2f7b2e1a690e3b464253dcde38041f3ee5504d6b075768d9672b26b6"},"schema_version":"1.0"},"canonical_sha256":"0ea54c774f195c0905e35304a51cee14fd8b28dfc0ef0cbe096ea04499a62fbe","source":{"kind":"arxiv","id":"1206.0152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0152","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0152v1","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0152","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"B2SUY52PDFOA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B2SUY52PDFOASBPD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B2SUY52P","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B2SUY52PDFOASBPDKMCKKHHOCT","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-01T11:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"f025a0795c20552883cd3785231412639a250caab8ab5f3753b96f8e1f312809","abstract_canon_sha256":"ba123cac2f7b2e1a690e3b464253dcde38041f3ee5504d6b075768d9672b26b6"},"schema_version":"1.0"},"canonical_sha256":"0ea54c774f195c0905e35304a51cee14fd8b28dfc0ef0cbe096ea04499a62fbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:26.972967Z","signature_b64":"WcRX8EGTwUoVN/Q1oKkKHDut+pitP1DgPNN7sjEnuSdSHWrwkFBgnLf1z6fnjzLeYxqlPU0wEqg29imWYNUZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ea54c774f195c0905e35304a51cee14fd8b28dfc0ef0cbe096ea04499a62fbe","last_reissued_at":"2026-05-18T03:54:26.972444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:26.972444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0152","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":"2026-05-18T03:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/h5+vnzuwVjw4EeH/mINbjvsw9KvnDtnZdRaecW86dhheXE7BPoV/6MUsHcbDP9BeOpQoOcQuYlfDAyTRcxdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:25:49.971885Z"},"content_sha256":"2fecb3d9e2975f7cdd1f6a3946ed2741cc1175c9a90732f615c8846b9da832fe","schema_version":"1.0","event_id":"sha256:2fecb3d9e2975f7cdd1f6a3946ed2741cc1175c9a90732f615c8846b9da832fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B2SUY52PDFOASBPDKMCKKHHOCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polymetric brick wall patterns and two-dimensional substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michel Dekking","submitted_at":"2012-06-01T11:33:51Z","abstract_excerpt":"Polymetric walls are walls built from bricks in more than one size. Architects and builders want to built polymetric walls that satisfy certain structural and aesthetical constraints. In a recent paper by de Jong, Vinduska, Hans and Post these problems are solved by integer programming techniques, which can be very time consuming for patterns consisting of more than 40 bricks. Here we give an extremely fast method, generating patterns of arbitrary size."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0152","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":"2026-05-18T03:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"omqd5/OzcIKvw0ScofF/+RtjyyY9Weg9GUMlR15fr/wRE/VDMWPSeunP9fZNexsjIgL4TUpnM7t+/YwrKCaUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:25:49.972605Z"},"content_sha256":"09506651b9e3f90aad48e2a2195cbbdc0665c67bee226498e4372749c02dcd5f","schema_version":"1.0","event_id":"sha256:09506651b9e3f90aad48e2a2195cbbdc0665c67bee226498e4372749c02dcd5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2SUY52PDFOASBPDKMCKKHHOCT/bundle.json","state_url":"https://pith.science/pith/B2SUY52PDFOASBPDKMCKKHHOCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2SUY52PDFOASBPDKMCKKHHOCT/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":"2026-05-30T15:25:49Z","links":{"resolver":"https://pith.science/pith/B2SUY52PDFOASBPDKMCKKHHOCT","bundle":"https://pith.science/pith/B2SUY52PDFOASBPDKMCKKHHOCT/bundle.json","state":"https://pith.science/pith/B2SUY52PDFOASBPDKMCKKHHOCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2SUY52PDFOASBPDKMCKKHHOCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B2SUY52PDFOASBPDKMCKKHHOCT","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":"ba123cac2f7b2e1a690e3b464253dcde38041f3ee5504d6b075768d9672b26b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-01T11:33:51Z","title_canon_sha256":"f025a0795c20552883cd3785231412639a250caab8ab5f3753b96f8e1f312809"},"schema_version":"1.0","source":{"id":"1206.0152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0152","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0152v1","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0152","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"B2SUY52PDFOA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B2SUY52PDFOASBPD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B2SUY52P","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:09506651b9e3f90aad48e2a2195cbbdc0665c67bee226498e4372749c02dcd5f","target":"graph","created_at":"2026-05-18T03:54:26Z","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":"Polymetric walls are walls built from bricks in more than one size. Architects and builders want to built polymetric walls that satisfy certain structural and aesthetical constraints. In a recent paper by de Jong, Vinduska, Hans and Post these problems are solved by integer programming techniques, which can be very time consuming for patterns consisting of more than 40 bricks. Here we give an extremely fast method, generating patterns of arbitrary size.","authors_text":"Michel Dekking","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-01T11:33:51Z","title":"Polymetric brick wall patterns and two-dimensional substitutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0152","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":"sha256:2fecb3d9e2975f7cdd1f6a3946ed2741cc1175c9a90732f615c8846b9da832fe","target":"record","created_at":"2026-05-18T03:54:26Z","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":"ba123cac2f7b2e1a690e3b464253dcde38041f3ee5504d6b075768d9672b26b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-01T11:33:51Z","title_canon_sha256":"f025a0795c20552883cd3785231412639a250caab8ab5f3753b96f8e1f312809"},"schema_version":"1.0","source":{"id":"1206.0152","kind":"arxiv","version":1}},"canonical_sha256":"0ea54c774f195c0905e35304a51cee14fd8b28dfc0ef0cbe096ea04499a62fbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ea54c774f195c0905e35304a51cee14fd8b28dfc0ef0cbe096ea04499a62fbe","first_computed_at":"2026-05-18T03:54:26.972444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:26.972444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WcRX8EGTwUoVN/Q1oKkKHDut+pitP1DgPNN7sjEnuSdSHWrwkFBgnLf1z6fnjzLeYxqlPU0wEqg29imWYNUZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:26.972967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fecb3d9e2975f7cdd1f6a3946ed2741cc1175c9a90732f615c8846b9da832fe","sha256:09506651b9e3f90aad48e2a2195cbbdc0665c67bee226498e4372749c02dcd5f"],"state_sha256":"a28a2df0360d46e84dc3f268dc9df38e6268e0b8466ca2ca01bd0c03cac0e525"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a52qBCnFLd3wLMV9/fam1RMfFM0KTx71XO1a9DsKp9AkWGGzyt49Jn4ldrlVlIs7cHNsURGe9KDiNddQLTKLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:25:49.977974Z","bundle_sha256":"ef5b45bac9855629171f1c3829b542a7bbeb2c1b9bc5c281fc39baac9da5fdd3"}}