{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SBQPSKTEXEXNOZHEVLKEKCQENG","short_pith_number":"pith:SBQPSKTE","canonical_record":{"source":{"id":"1208.5752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T19:15:33Z","cross_cats_sorted":["cond-mat.soft","cs.CG"],"title_canon_sha256":"7326b63ecdba15f06dc3c34c47ab725cd062c3982d79cbf98a811bcd3101ab72","abstract_canon_sha256":"df5474dc6d7e87f7a5a2e0f6af6f7caa65d6f078039cb3a37971b4c1c9f5ed95"},"schema_version":"1.0"},"canonical_sha256":"9060f92a64b92ed764e4aad4450a0469955522485285de14738fd72ac00639b8","source":{"kind":"arxiv","id":"1208.5752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5752","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5752v1","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5752","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"SBQPSKTEXEXN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SBQPSKTEXEXNOZHE","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SBQPSKTE","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SBQPSKTEXEXNOZHEVLKEKCQENG","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T19:15:33Z","cross_cats_sorted":["cond-mat.soft","cs.CG"],"title_canon_sha256":"7326b63ecdba15f06dc3c34c47ab725cd062c3982d79cbf98a811bcd3101ab72","abstract_canon_sha256":"df5474dc6d7e87f7a5a2e0f6af6f7caa65d6f078039cb3a37971b4c1c9f5ed95"},"schema_version":"1.0"},"canonical_sha256":"9060f92a64b92ed764e4aad4450a0469955522485285de14738fd72ac00639b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:57.857097Z","signature_b64":"sWrvRs0G3ruQx7mcQwh/E92XcjQK60bKnVhyiBzgZWDaPMEJNrCe7XX6KW9u4EfCBZT1Vv8Y50LcldfbcD+JCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9060f92a64b92ed764e4aad4450a0469955522485285de14738fd72ac00639b8","last_reissued_at":"2026-05-18T03:46:57.856606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:57.856606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5752","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":"2026-05-18T03:46:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"89sjOzRa+wqhfUjLerc+r7919qqQORuSzVTx7KL1ICqvYg4tp/bsUulN+bhlDFfylFfuRBymHSktnMzFRsQkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:46:28.280353Z"},"content_sha256":"08cf13b711b60859182664639fa0f1a2a492c61007862a8e429568cb4ee7d1e2","schema_version":"1.0","event_id":"sha256:08cf13b711b60859182664639fa0f1a2a492c61007862a8e429568cb4ee7d1e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SBQPSKTEXEXNOZHEVLKEKCQENG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Fillings - A new spatial subdivision problem related to packing and covering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","cs.CG"],"primary_cat":"math.OC","authors_text":"Carolyn L. Phillips, Elizabeth R. Chen, Joshua A. Anderson, Sharon C. Glotzer","submitted_at":"2012-08-28T19:15:33Z","abstract_excerpt":"We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls and the solution space can reduced to the medial axis of a shape. We examine the structure of the solution space in two dimensions. For the filling of polygons, we provide detailed descriptions of a heuristic and a genetic a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5752","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":"2026-05-18T03:46:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mBCPZaXm3deoBBnBkk+Je/cf4mkoqqICnJr1wb6Sc15CSWXE2HaXyg0UerNkZ6usLI024k2Fu3ST3gYm6RRpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:46:28.281094Z"},"content_sha256":"729d20efd660b2901c5893f3b6ded9190e0fb01de1b1dfb7d9ec411df6f4c193","schema_version":"1.0","event_id":"sha256:729d20efd660b2901c5893f3b6ded9190e0fb01de1b1dfb7d9ec411df6f4c193"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBQPSKTEXEXNOZHEVLKEKCQENG/bundle.json","state_url":"https://pith.science/pith/SBQPSKTEXEXNOZHEVLKEKCQENG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBQPSKTEXEXNOZHEVLKEKCQENG/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":"2026-05-27T06:46:28Z","links":{"resolver":"https://pith.science/pith/SBQPSKTEXEXNOZHEVLKEKCQENG","bundle":"https://pith.science/pith/SBQPSKTEXEXNOZHEVLKEKCQENG/bundle.json","state":"https://pith.science/pith/SBQPSKTEXEXNOZHEVLKEKCQENG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBQPSKTEXEXNOZHEVLKEKCQENG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SBQPSKTEXEXNOZHEVLKEKCQENG","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":"df5474dc6d7e87f7a5a2e0f6af6f7caa65d6f078039cb3a37971b4c1c9f5ed95","cross_cats_sorted":["cond-mat.soft","cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T19:15:33Z","title_canon_sha256":"7326b63ecdba15f06dc3c34c47ab725cd062c3982d79cbf98a811bcd3101ab72"},"schema_version":"1.0","source":{"id":"1208.5752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5752","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5752v1","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5752","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"SBQPSKTEXEXN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SBQPSKTEXEXNOZHE","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SBQPSKTE","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:729d20efd660b2901c5893f3b6ded9190e0fb01de1b1dfb7d9ec411df6f4c193","target":"graph","created_at":"2026-05-18T03:46:57Z","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 present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls and the solution space can reduced to the medial axis of a shape. We examine the structure of the solution space in two dimensions. For the filling of polygons, we provide detailed descriptions of a heuristic and a genetic a","authors_text":"Carolyn L. Phillips, Elizabeth R. Chen, Joshua A. Anderson, Sharon C. Glotzer","cross_cats":["cond-mat.soft","cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T19:15:33Z","title":"Optimal Fillings - A new spatial subdivision problem related to packing and covering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5752","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":"sha256:08cf13b711b60859182664639fa0f1a2a492c61007862a8e429568cb4ee7d1e2","target":"record","created_at":"2026-05-18T03:46:57Z","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":"df5474dc6d7e87f7a5a2e0f6af6f7caa65d6f078039cb3a37971b4c1c9f5ed95","cross_cats_sorted":["cond-mat.soft","cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T19:15:33Z","title_canon_sha256":"7326b63ecdba15f06dc3c34c47ab725cd062c3982d79cbf98a811bcd3101ab72"},"schema_version":"1.0","source":{"id":"1208.5752","kind":"arxiv","version":1}},"canonical_sha256":"9060f92a64b92ed764e4aad4450a0469955522485285de14738fd72ac00639b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9060f92a64b92ed764e4aad4450a0469955522485285de14738fd72ac00639b8","first_computed_at":"2026-05-18T03:46:57.856606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:57.856606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sWrvRs0G3ruQx7mcQwh/E92XcjQK60bKnVhyiBzgZWDaPMEJNrCe7XX6KW9u4EfCBZT1Vv8Y50LcldfbcD+JCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:57.857097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08cf13b711b60859182664639fa0f1a2a492c61007862a8e429568cb4ee7d1e2","sha256:729d20efd660b2901c5893f3b6ded9190e0fb01de1b1dfb7d9ec411df6f4c193"],"state_sha256":"ee26660865e77e4d9ed0c37964fc7cc3b51144c24a6cab649242d1bf69e45ea3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fs5KmE0NCZJ1487SoNF6T93mqQSqnQTxc9PA2czLfP1GM/XRhmhypuInOrgtNKcPxaXhpiQmgNkysyIDH6DmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:46:28.284871Z","bundle_sha256":"c3f6f93add138174de684f0a723788cd476d95a44cd0032851371a5e3c246214"}}