{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YH3SW3YRXZXZCR7YQ4DRWPCEQD","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":"da7661af0c79fcb9eee171095dcc7f672d663d4faee1510c5c7711f6be95fe0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-05-26T09:22:03Z","title_canon_sha256":"26930cdcd1b54833021adfe027c28482d6c6455960eaff69741293e0335c76dd"},"schema_version":"1.0","source":{"id":"1505.07300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07300","created_at":"2026-05-18T01:28:04Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07300v1","created_at":"2026-05-18T01:28:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07300","created_at":"2026-05-18T01:28:04Z"},{"alias_kind":"pith_short_12","alias_value":"YH3SW3YRXZXZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YH3SW3YRXZXZCR7Y","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YH3SW3YR","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:70a990089bb20d4c718d79d40f41b2b8fc7cf719286c2cb100008c433d23cf57","target":"graph","created_at":"2026-05-18T01:28:04Z","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":"The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Pet","authors_text":"An-Chang Shi, Jiajun Tong, Kai Jiang, Pingwen Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-05-26T09:22:03Z","title":"Stability of Two-Dimensional Soft Quasicrystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07300","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":"sha256:2644c6bb3f344c37b32f460265d692465c4b0c234c1ee3e22c680552a38eed7c","target":"record","created_at":"2026-05-18T01:28:04Z","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":"da7661af0c79fcb9eee171095dcc7f672d663d4faee1510c5c7711f6be95fe0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-05-26T09:22:03Z","title_canon_sha256":"26930cdcd1b54833021adfe027c28482d6c6455960eaff69741293e0335c76dd"},"schema_version":"1.0","source":{"id":"1505.07300","kind":"arxiv","version":1}},"canonical_sha256":"c1f72b6f11be6f9147f887071b3c4480ec2600bb764b59b3d7475bafb8989874","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1f72b6f11be6f9147f887071b3c4480ec2600bb764b59b3d7475bafb8989874","first_computed_at":"2026-05-18T01:28:04.908043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:04.908043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/boSvaWuYsYV+vqjP2KRtgUpgmxpqtW9/p2PiIsYSGoVYKcwNxOkPfSWIRPabNHofgBUHQUXIPbmsDSVxpa4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:04.908698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2644c6bb3f344c37b32f460265d692465c4b0c234c1ee3e22c680552a38eed7c","sha256:70a990089bb20d4c718d79d40f41b2b8fc7cf719286c2cb100008c433d23cf57"],"state_sha256":"a2ce1f7575b1c2835eb84c4095fe22b3c3df34502c5534df09c693e090cdcb29"}