{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XNSLHHM2NPBFTFYGNGVTFV5CDN","short_pith_number":"pith:XNSLHHM2","canonical_record":{"source":{"id":"1111.3004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2011-11-13T12:37:27Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"f4325ad9895d913ce2e401558cc79edcfaf6d6b4e8588e432426077102c46dd8","abstract_canon_sha256":"7fd6c78dfd14ca391322a8cbe3b9b2fbd769ab8c86a77cb9028d40ac439cdd5b"},"schema_version":"1.0"},"canonical_sha256":"bb64b39d9a6bc259970669ab32d7a21b716a49e7fd6d94dc305739781f87c2cf","source":{"kind":"arxiv","id":"1111.3004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3004","created_at":"2026-05-18T04:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3004v1","created_at":"2026-05-18T04:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3004","created_at":"2026-05-18T04:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"XNSLHHM2NPBF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XNSLHHM2NPBFTFYG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XNSLHHM2","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XNSLHHM2NPBFTFYGNGVTFV5CDN","target":"record","payload":{"canonical_record":{"source":{"id":"1111.3004","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2011-11-13T12:37:27Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"f4325ad9895d913ce2e401558cc79edcfaf6d6b4e8588e432426077102c46dd8","abstract_canon_sha256":"7fd6c78dfd14ca391322a8cbe3b9b2fbd769ab8c86a77cb9028d40ac439cdd5b"},"schema_version":"1.0"},"canonical_sha256":"bb64b39d9a6bc259970669ab32d7a21b716a49e7fd6d94dc305739781f87c2cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:11.323286Z","signature_b64":"1K7zfFqY8DijNkFhYe20wKzaJwF1ImkrUladSHmSPcYhBW3jfyQO9piNGxxJbDwcO8AzMrk6nNgBPg5uvjK7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb64b39d9a6bc259970669ab32d7a21b716a49e7fd6d94dc305739781f87c2cf","last_reissued_at":"2026-05-18T04:01:11.322619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:11.322619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.3004","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":"2026-05-18T04:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3W2U1VYPjUZj/dvEsZjwRCqmRH3vaaYOCmrnm3f4UKD4JhSgmQAZFXkmfDQa5YwKUyDjStLcFmfO5ZJ7tIGbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:35:14.498504Z"},"content_sha256":"e4bfa665cacfc3dcc19db8a366041ce110fd34534b6edc003d467e68d53a21b4","schema_version":"1.0","event_id":"sha256:e4bfa665cacfc3dcc19db8a366041ce110fd34534b6edc003d467e68d53a21b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XNSLHHM2NPBFTFYGNGVTFV5CDN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry Breaking and Order in the Age of Quasicrystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Ron Lifshitz","submitted_at":"2011-11-13T12:37:27Z","abstract_excerpt":"The discovery of quasicrystals has changed our view of some of the most basic notions related to the condensed state of matter. Before the age of quasicrystals, it was believed that crystals break the continuous translation and rotation symmetries of the liquid-phase into a discrete lattice of translations, and a finite group of rotations. Quasicrystals, on the other hand, possess no such symmetries-there are no translations, nor, in general, are there any rotations, leaving them invariant. Does this imply that no symmetry is left, or that the meaning of symmetry should be revised? We review t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3004","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":"2026-05-18T04:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IMfIFePlykXPULW92BqzSNdMg8DZzd9wLJMHUtTeNatCwIoJSdfbrJNiBHB/CyCrmicj9ivm/pQgm0myhV9eCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:35:14.499352Z"},"content_sha256":"617f0bd4aed36672df8118c1a49739f7dd8998859c9c350c86ef5c86c31e8baa","schema_version":"1.0","event_id":"sha256:617f0bd4aed36672df8118c1a49739f7dd8998859c9c350c86ef5c86c31e8baa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN/bundle.json","state_url":"https://pith.science/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN/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":"2026-06-10T01:35:14Z","links":{"resolver":"https://pith.science/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN","bundle":"https://pith.science/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN/bundle.json","state":"https://pith.science/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNSLHHM2NPBFTFYGNGVTFV5CDN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XNSLHHM2NPBFTFYGNGVTFV5CDN","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":"7fd6c78dfd14ca391322a8cbe3b9b2fbd769ab8c86a77cb9028d40ac439cdd5b","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2011-11-13T12:37:27Z","title_canon_sha256":"f4325ad9895d913ce2e401558cc79edcfaf6d6b4e8588e432426077102c46dd8"},"schema_version":"1.0","source":{"id":"1111.3004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3004","created_at":"2026-05-18T04:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3004v1","created_at":"2026-05-18T04:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3004","created_at":"2026-05-18T04:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"XNSLHHM2NPBF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XNSLHHM2NPBFTFYG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XNSLHHM2","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:617f0bd4aed36672df8118c1a49739f7dd8998859c9c350c86ef5c86c31e8baa","target":"graph","created_at":"2026-05-18T04:01:11Z","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 discovery of quasicrystals has changed our view of some of the most basic notions related to the condensed state of matter. Before the age of quasicrystals, it was believed that crystals break the continuous translation and rotation symmetries of the liquid-phase into a discrete lattice of translations, and a finite group of rotations. Quasicrystals, on the other hand, possess no such symmetries-there are no translations, nor, in general, are there any rotations, leaving them invariant. Does this imply that no symmetry is left, or that the meaning of symmetry should be revised? We review t","authors_text":"Ron Lifshitz","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2011-11-13T12:37:27Z","title":"Symmetry Breaking and Order in the Age of Quasicrystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3004","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:e4bfa665cacfc3dcc19db8a366041ce110fd34534b6edc003d467e68d53a21b4","target":"record","created_at":"2026-05-18T04:01:11Z","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":"7fd6c78dfd14ca391322a8cbe3b9b2fbd769ab8c86a77cb9028d40ac439cdd5b","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2011-11-13T12:37:27Z","title_canon_sha256":"f4325ad9895d913ce2e401558cc79edcfaf6d6b4e8588e432426077102c46dd8"},"schema_version":"1.0","source":{"id":"1111.3004","kind":"arxiv","version":1}},"canonical_sha256":"bb64b39d9a6bc259970669ab32d7a21b716a49e7fd6d94dc305739781f87c2cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb64b39d9a6bc259970669ab32d7a21b716a49e7fd6d94dc305739781f87c2cf","first_computed_at":"2026-05-18T04:01:11.322619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:11.322619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1K7zfFqY8DijNkFhYe20wKzaJwF1ImkrUladSHmSPcYhBW3jfyQO9piNGxxJbDwcO8AzMrk6nNgBPg5uvjK7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:11.323286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4bfa665cacfc3dcc19db8a366041ce110fd34534b6edc003d467e68d53a21b4","sha256:617f0bd4aed36672df8118c1a49739f7dd8998859c9c350c86ef5c86c31e8baa"],"state_sha256":"94c7876071246ee6c56039b0792e7e3afaa648a401ed1bfb315fbff2ab80f39b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJ+shwTD/CF5aVk95OKc1EibfDRC87mqH1T71UyHTyLLcAbD+ArX26d2a8bx9w15GX17xTGl2EbPF91pCldIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:35:14.503525Z","bundle_sha256":"6c5293060deda8e602f02d8f922511c906e794bfc1fce92a790f5314482d6c63"}}