{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4U23LJPYWXC7FDWKWCN3CMQBQR","short_pith_number":"pith:4U23LJPY","canonical_record":{"source":{"id":"1104.2809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-04-14T15:46:11Z","cross_cats_sorted":["cs.CC","cs.DS","cs.ET"],"title_canon_sha256":"448be3d6f6cafb26b57cbf2373e361ddba9c38a44e675ab3cb0e8376551fda83","abstract_canon_sha256":"f9dbc0f7aa0345876debc9c6353c51ecbb3c9d0e78e827d10136a0c9f687ae7f"},"schema_version":"1.0"},"canonical_sha256":"e535b5a5f8b5c5f28ecab09bb132018477bbcdd86d677e6629476bbfaaa1e496","source":{"kind":"arxiv","id":"1104.2809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2809","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2809v1","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2809","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"4U23LJPYWXC7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4U23LJPYWXC7FDWK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4U23LJPY","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4U23LJPYWXC7FDWKWCN3CMQBQR","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-04-14T15:46:11Z","cross_cats_sorted":["cs.CC","cs.DS","cs.ET"],"title_canon_sha256":"448be3d6f6cafb26b57cbf2373e361ddba9c38a44e675ab3cb0e8376551fda83","abstract_canon_sha256":"f9dbc0f7aa0345876debc9c6353c51ecbb3c9d0e78e827d10136a0c9f687ae7f"},"schema_version":"1.0"},"canonical_sha256":"e535b5a5f8b5c5f28ecab09bb132018477bbcdd86d677e6629476bbfaaa1e496","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:09.175410Z","signature_b64":"TivEE4NvqZyni0HfycA1Ziw+bJFHnMCZ+iy2P7sn9ReT0JOhvmdwK927O5FrTLrEWt25A1hrdyb10WeU9M+8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e535b5a5f8b5c5f28ecab09bb132018477bbcdd86d677e6629476bbfaaa1e496","last_reissued_at":"2026-05-18T02:22:09.174879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:09.174879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2809","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":"2026-05-18T02:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UXJ11RQTAHrqPbPrehb5fIsKzPboewz0Ic1wuvo9qf+WIMm/nMWcXa1gvyyz4HMJZszbelesrmPKzQrKE2SADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:24:55.238426Z"},"content_sha256":"68c418879be6b2a2d9acef67687ce0b1571c3cb9dded3b4b1a964c2327c7309a","schema_version":"1.0","event_id":"sha256:68c418879be6b2a2d9acef67687ce0b1571c3cb9dded3b4b1a964c2327c7309a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4U23LJPYWXC7FDWKWCN3CMQBQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Assembly with Geometric Tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","cs.ET"],"primary_cat":"cs.CG","authors_text":"Bin Fu, Bobby Sheline, Matthew J. Patitz, Robert T. Schweller","submitted_at":"2011-04-14T15:46:11Z","abstract_excerpt":"In this work we propose a generalization of Winfree's abstract Tile Assembly Model (aTAM) in which tile types are assigned rigid shapes, or geometries, along each tile face. We examine the number of distinct tile types needed to assemble shapes within this model, the temperature required for efficient assembly, and the problem of designing compact geometric faces to meet given compatibility specifications. Our results show a dramatic decrease in the number of tile types needed to assemble $n \\times n$ squares to $\\Theta(\\sqrt{\\log n})$ at temperature 1 for the most simple model which meets a l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2809","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":"2026-05-18T02:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Na4Va6TL1J5rfzFAxm+CRhPcXAKTGCdR6jwPLyhlL1yi7KudxE78kXyLkfz6mj/JMC1OzpMIDAv4Dvy8e/xCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:24:55.238797Z"},"content_sha256":"fd75ba812a00fe0203607c476a8b2cabcebfcad477f919c4864b39ddb509a27a","schema_version":"1.0","event_id":"sha256:fd75ba812a00fe0203607c476a8b2cabcebfcad477f919c4864b39ddb509a27a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4U23LJPYWXC7FDWKWCN3CMQBQR/bundle.json","state_url":"https://pith.science/pith/4U23LJPYWXC7FDWKWCN3CMQBQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4U23LJPYWXC7FDWKWCN3CMQBQR/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":"2026-05-28T09:24:55Z","links":{"resolver":"https://pith.science/pith/4U23LJPYWXC7FDWKWCN3CMQBQR","bundle":"https://pith.science/pith/4U23LJPYWXC7FDWKWCN3CMQBQR/bundle.json","state":"https://pith.science/pith/4U23LJPYWXC7FDWKWCN3CMQBQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4U23LJPYWXC7FDWKWCN3CMQBQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4U23LJPYWXC7FDWKWCN3CMQBQR","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":"f9dbc0f7aa0345876debc9c6353c51ecbb3c9d0e78e827d10136a0c9f687ae7f","cross_cats_sorted":["cs.CC","cs.DS","cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-04-14T15:46:11Z","title_canon_sha256":"448be3d6f6cafb26b57cbf2373e361ddba9c38a44e675ab3cb0e8376551fda83"},"schema_version":"1.0","source":{"id":"1104.2809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2809","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2809v1","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2809","created_at":"2026-05-18T02:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"4U23LJPYWXC7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4U23LJPYWXC7FDWK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4U23LJPY","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:fd75ba812a00fe0203607c476a8b2cabcebfcad477f919c4864b39ddb509a27a","target":"graph","created_at":"2026-05-18T02:22:09Z","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":"In this work we propose a generalization of Winfree's abstract Tile Assembly Model (aTAM) in which tile types are assigned rigid shapes, or geometries, along each tile face. We examine the number of distinct tile types needed to assemble shapes within this model, the temperature required for efficient assembly, and the problem of designing compact geometric faces to meet given compatibility specifications. Our results show a dramatic decrease in the number of tile types needed to assemble $n \\times n$ squares to $\\Theta(\\sqrt{\\log n})$ at temperature 1 for the most simple model which meets a l","authors_text":"Bin Fu, Bobby Sheline, Matthew J. Patitz, Robert T. Schweller","cross_cats":["cs.CC","cs.DS","cs.ET"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-04-14T15:46:11Z","title":"Self-Assembly with Geometric Tiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2809","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":"sha256:68c418879be6b2a2d9acef67687ce0b1571c3cb9dded3b4b1a964c2327c7309a","target":"record","created_at":"2026-05-18T02:22:09Z","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":"f9dbc0f7aa0345876debc9c6353c51ecbb3c9d0e78e827d10136a0c9f687ae7f","cross_cats_sorted":["cs.CC","cs.DS","cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-04-14T15:46:11Z","title_canon_sha256":"448be3d6f6cafb26b57cbf2373e361ddba9c38a44e675ab3cb0e8376551fda83"},"schema_version":"1.0","source":{"id":"1104.2809","kind":"arxiv","version":1}},"canonical_sha256":"e535b5a5f8b5c5f28ecab09bb132018477bbcdd86d677e6629476bbfaaa1e496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e535b5a5f8b5c5f28ecab09bb132018477bbcdd86d677e6629476bbfaaa1e496","first_computed_at":"2026-05-18T02:22:09.174879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:09.174879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TivEE4NvqZyni0HfycA1Ziw+bJFHnMCZ+iy2P7sn9ReT0JOhvmdwK927O5FrTLrEWt25A1hrdyb10WeU9M+8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:09.175410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68c418879be6b2a2d9acef67687ce0b1571c3cb9dded3b4b1a964c2327c7309a","sha256:fd75ba812a00fe0203607c476a8b2cabcebfcad477f919c4864b39ddb509a27a"],"state_sha256":"2e8fd5705818bb412a12cdf5e4a8d849ed501bcb915fe378fa7a228da365d566"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vDSOSHnxvVlim83UM2irk6AmCGxuIx4+UKLm/Yg9c2BlhP45pP0OyY5qRARiMCiPVS9Bdo/fOWidM3tScURFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:24:55.240972Z","bundle_sha256":"1ae871c8493d16d623bd53afb07ff779615945935236346a4b9b3fad5e9e9a82"}}