{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PAMQ5W5ZHN636WW5GDSJGHNNCX","short_pith_number":"pith:PAMQ5W5Z","canonical_record":{"source":{"id":"1112.4087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-17T21:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"7d5594afa4ec48bc2b62747811fd6bad790d815d5a2f54cea152ec3ef2a445e1","abstract_canon_sha256":"091b646f4029ace93f628443242c88a767fd1595363922b2a489d315b98c8852"},"schema_version":"1.0"},"canonical_sha256":"78190edbb93b7dbf5add30e4931dad15c3270bb490a7c21270ba716db0cc8356","source":{"kind":"arxiv","id":"1112.4087","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4087","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4087v1","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4087","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"PAMQ5W5ZHN63","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PAMQ5W5ZHN636WW5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PAMQ5W5Z","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PAMQ5W5ZHN636WW5GDSJGHNNCX","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-17T21:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"7d5594afa4ec48bc2b62747811fd6bad790d815d5a2f54cea152ec3ef2a445e1","abstract_canon_sha256":"091b646f4029ace93f628443242c88a767fd1595363922b2a489d315b98c8852"},"schema_version":"1.0"},"canonical_sha256":"78190edbb93b7dbf5add30e4931dad15c3270bb490a7c21270ba716db0cc8356","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:07.042268Z","signature_b64":"hu3jCEcv1df0jAHTh6xKOTCe/b3sMkeffBdqf9+3ZWAv9tZN3fOfO2+4+p+rT5m3HDfD6D+0Qc8/aVYM6NcMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78190edbb93b7dbf5add30e4931dad15c3270bb490a7c21270ba716db0cc8356","last_reissued_at":"2026-05-18T04:06:07.041844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:07.041844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4087","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":"2026-05-18T04:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JDu8n4m0PmCyuQPdl8/H/FVX+N9kTFseZ9OH0tBmhGLhbEpfH8xGXsPWBw5OQotDzod9K8/fS6pIxR0Kd/l+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:36:06.338433Z"},"content_sha256":"dba8fd5eb65d4baadc2f2c7603420efc9be1b0ef3f34c2728bae7a00cbe5adca","schema_version":"1.0","event_id":"sha256:dba8fd5eb65d4baadc2f2c7603420efc9be1b0ef3f34c2728bae7a00cbe5adca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PAMQ5W5ZHN636WW5GDSJGHNNCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of Interlocking Polyominoes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sidharth Dhawan, Zachary Abel","submitted_at":"2011-12-17T21:11:52Z","abstract_excerpt":"Polyominoes are a subset of polygons which can be constructed from integer-length squares fused at their edges. A system of polygons P is interlocked if no subset of the polygons in P can be removed arbitrarily far away from the rest. It is already known that polyominoes with four or fewer squares cannot interlock. It is also known that determining the interlockedness of polyominoes with an arbitrary number of squares is PSPACE hard. Here, we prove that a system of polyominoes with five or fewer squares cannot interlock, and that determining interlockedness of a system of polyominoes including"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4087","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":"2026-05-18T04:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GXf57EMwazrqvfssQ2nsTHHdFG+GJF/6niUyv1BIEmIqAoDXg43TQ1IpiOyhskXbtcjMJ9fS/DCmudyqlroAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:36:06.338824Z"},"content_sha256":"e75a303f994b64d54fbfef6394c1aecefedc74c8bd92ee393018ee17b034e001","schema_version":"1.0","event_id":"sha256:e75a303f994b64d54fbfef6394c1aecefedc74c8bd92ee393018ee17b034e001"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX/bundle.json","state_url":"https://pith.science/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX/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":"2026-05-31T23:36:06Z","links":{"resolver":"https://pith.science/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX","bundle":"https://pith.science/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX/bundle.json","state":"https://pith.science/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PAMQ5W5ZHN636WW5GDSJGHNNCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PAMQ5W5ZHN636WW5GDSJGHNNCX","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":"091b646f4029ace93f628443242c88a767fd1595363922b2a489d315b98c8852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-17T21:11:52Z","title_canon_sha256":"7d5594afa4ec48bc2b62747811fd6bad790d815d5a2f54cea152ec3ef2a445e1"},"schema_version":"1.0","source":{"id":"1112.4087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4087","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4087v1","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4087","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"PAMQ5W5ZHN63","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PAMQ5W5ZHN636WW5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PAMQ5W5Z","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:e75a303f994b64d54fbfef6394c1aecefedc74c8bd92ee393018ee17b034e001","target":"graph","created_at":"2026-05-18T04:06:07Z","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":"Polyominoes are a subset of polygons which can be constructed from integer-length squares fused at their edges. A system of polygons P is interlocked if no subset of the polygons in P can be removed arbitrarily far away from the rest. It is already known that polyominoes with four or fewer squares cannot interlock. It is also known that determining the interlockedness of polyominoes with an arbitrary number of squares is PSPACE hard. Here, we prove that a system of polyominoes with five or fewer squares cannot interlock, and that determining interlockedness of a system of polyominoes including","authors_text":"Sidharth Dhawan, Zachary Abel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-17T21:11:52Z","title":"Complexity of Interlocking Polyominoes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4087","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:dba8fd5eb65d4baadc2f2c7603420efc9be1b0ef3f34c2728bae7a00cbe5adca","target":"record","created_at":"2026-05-18T04:06:07Z","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":"091b646f4029ace93f628443242c88a767fd1595363922b2a489d315b98c8852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-17T21:11:52Z","title_canon_sha256":"7d5594afa4ec48bc2b62747811fd6bad790d815d5a2f54cea152ec3ef2a445e1"},"schema_version":"1.0","source":{"id":"1112.4087","kind":"arxiv","version":1}},"canonical_sha256":"78190edbb93b7dbf5add30e4931dad15c3270bb490a7c21270ba716db0cc8356","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78190edbb93b7dbf5add30e4931dad15c3270bb490a7c21270ba716db0cc8356","first_computed_at":"2026-05-18T04:06:07.041844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:07.041844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hu3jCEcv1df0jAHTh6xKOTCe/b3sMkeffBdqf9+3ZWAv9tZN3fOfO2+4+p+rT5m3HDfD6D+0Qc8/aVYM6NcMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:07.042268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dba8fd5eb65d4baadc2f2c7603420efc9be1b0ef3f34c2728bae7a00cbe5adca","sha256:e75a303f994b64d54fbfef6394c1aecefedc74c8bd92ee393018ee17b034e001"],"state_sha256":"6e412671721487a2fcdf7f7dfd81ad7b8620336d90b22bd732dbdca190435279"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSxqdf0FB0gvgisL8EnhRcTs7XBE0u5iSgJE8SpSCT53cDowCYGs5fsCAYZe1jrqDGptcEUatN/XHyHU+e+DBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:36:06.341148Z","bundle_sha256":"f20749f5bd1e2d261cb9a331e756b56274d2407d56c1040e665ea01ed7602d5d"}}