{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C4TPALRVFZHKHTDVSXTLQEUNUG","short_pith_number":"pith:C4TPALRV","canonical_record":{"source":{"id":"1608.08315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2016-08-30T03:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"09615b9d88edd74cbc47c2b23c7bc7761d8817f6d7886e8cca567a00620b50e1","abstract_canon_sha256":"094ee5bd65c3542cfef3119ad3da8a582a92cdca2c009a2d883b03bbd2adb016"},"schema_version":"1.0"},"canonical_sha256":"1726f02e352e4ea3cc7595e6b8128da18453b479cd56e3df62f99006909de976","source":{"kind":"arxiv","id":"1608.08315","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08315","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08315v2","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08315","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"pith_short_12","alias_value":"C4TPALRVFZHK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C4TPALRVFZHKHTDV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C4TPALRV","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C4TPALRVFZHKHTDVSXTLQEUNUG","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2016-08-30T03:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"09615b9d88edd74cbc47c2b23c7bc7761d8817f6d7886e8cca567a00620b50e1","abstract_canon_sha256":"094ee5bd65c3542cfef3119ad3da8a582a92cdca2c009a2d883b03bbd2adb016"},"schema_version":"1.0"},"canonical_sha256":"1726f02e352e4ea3cc7595e6b8128da18453b479cd56e3df62f99006909de976","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:49.723142Z","signature_b64":"StiATjfyIF6r8MrIIXzB8QYl0z9Cyb8K+RVnUcHBfwW/3aF8otyO2k/GGU2+hY5L7cZGd0MP8lGvM7qTG6k3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1726f02e352e4ea3cc7595e6b8128da18453b479cd56e3df62f99006909de976","last_reissued_at":"2026-05-18T01:02:49.722592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:49.722592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08315","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbRcisaW0PE87U02Ilve6JGKVBK4omArBDYZJJ237NwFvNMXsR8N1BrnFbWpa1dq8n0bBhzni0qCBEa/67voBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:36:57.127556Z"},"content_sha256":"5e027ab19f7bef578c25c9cde5e85d3b43c8293d4b77f2a1d0eb8214f957c53f","schema_version":"1.0","event_id":"sha256:5e027ab19f7bef578c25c9cde5e85d3b43c8293d4b77f2a1d0eb8214f957c53f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C4TPALRVFZHKHTDVSXTLQEUNUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Direct calculation of the linear thermal expansion coefficients of MoS2 via symmetry-preserving deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Chee Kwan Gan, Yu Yang Fredrik Liu","submitted_at":"2016-08-30T03:37:49Z","abstract_excerpt":"Using density-functional perturbation theory and the Gr\\\"uneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS$_2$ in the crystallographic $a$ and $c$ directions. The TEC calculation depends critically on the evaluation of a temperature-dependent quantity $I_i(T)$, which is the integral of the product of heat capacity and $\\Gamma_i(\\nu)$, of frequency $\\nu$ and strain type $i$, where $\\Gamma_i(\\nu)$ is the phonon density of states weighted by the Gr\\\"uneisen parameters. We show that to determine the linear TECs we may use minim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08315","kind":"arxiv","version":2},"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":"2026-05-18T01:02:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AxBo8QV+LysTZWclZjBDYOgsuUXPtaCGqFHrrTgKf6I/do4waZ3WPq+yObKgAVTfyciJRW604GEZBRu5xteXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:36:57.127895Z"},"content_sha256":"8588e3be21fff843ba9e6f117a349e552efc8bf5121e173efd96460eceff41e6","schema_version":"1.0","event_id":"sha256:8588e3be21fff843ba9e6f117a349e552efc8bf5121e173efd96460eceff41e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4TPALRVFZHKHTDVSXTLQEUNUG/bundle.json","state_url":"https://pith.science/pith/C4TPALRVFZHKHTDVSXTLQEUNUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4TPALRVFZHKHTDVSXTLQEUNUG/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":"2026-06-29T06:36:57Z","links":{"resolver":"https://pith.science/pith/C4TPALRVFZHKHTDVSXTLQEUNUG","bundle":"https://pith.science/pith/C4TPALRVFZHKHTDVSXTLQEUNUG/bundle.json","state":"https://pith.science/pith/C4TPALRVFZHKHTDVSXTLQEUNUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4TPALRVFZHKHTDVSXTLQEUNUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C4TPALRVFZHKHTDVSXTLQEUNUG","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":"094ee5bd65c3542cfef3119ad3da8a582a92cdca2c009a2d883b03bbd2adb016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2016-08-30T03:37:49Z","title_canon_sha256":"09615b9d88edd74cbc47c2b23c7bc7761d8817f6d7886e8cca567a00620b50e1"},"schema_version":"1.0","source":{"id":"1608.08315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08315","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08315v2","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08315","created_at":"2026-05-18T01:02:49Z"},{"alias_kind":"pith_short_12","alias_value":"C4TPALRVFZHK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C4TPALRVFZHKHTDV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C4TPALRV","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:8588e3be21fff843ba9e6f117a349e552efc8bf5121e173efd96460eceff41e6","target":"graph","created_at":"2026-05-18T01:02:49Z","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":"Using density-functional perturbation theory and the Gr\\\"uneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS$_2$ in the crystallographic $a$ and $c$ directions. The TEC calculation depends critically on the evaluation of a temperature-dependent quantity $I_i(T)$, which is the integral of the product of heat capacity and $\\Gamma_i(\\nu)$, of frequency $\\nu$ and strain type $i$, where $\\Gamma_i(\\nu)$ is the phonon density of states weighted by the Gr\\\"uneisen parameters. We show that to determine the linear TECs we may use minim","authors_text":"Chee Kwan Gan, Yu Yang Fredrik Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2016-08-30T03:37:49Z","title":"Direct calculation of the linear thermal expansion coefficients of MoS2 via symmetry-preserving deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08315","kind":"arxiv","version":2},"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":"sha256:5e027ab19f7bef578c25c9cde5e85d3b43c8293d4b77f2a1d0eb8214f957c53f","target":"record","created_at":"2026-05-18T01:02:49Z","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":"094ee5bd65c3542cfef3119ad3da8a582a92cdca2c009a2d883b03bbd2adb016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2016-08-30T03:37:49Z","title_canon_sha256":"09615b9d88edd74cbc47c2b23c7bc7761d8817f6d7886e8cca567a00620b50e1"},"schema_version":"1.0","source":{"id":"1608.08315","kind":"arxiv","version":2}},"canonical_sha256":"1726f02e352e4ea3cc7595e6b8128da18453b479cd56e3df62f99006909de976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1726f02e352e4ea3cc7595e6b8128da18453b479cd56e3df62f99006909de976","first_computed_at":"2026-05-18T01:02:49.722592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:49.722592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"StiATjfyIF6r8MrIIXzB8QYl0z9Cyb8K+RVnUcHBfwW/3aF8otyO2k/GGU2+hY5L7cZGd0MP8lGvM7qTG6k3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:49.723142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e027ab19f7bef578c25c9cde5e85d3b43c8293d4b77f2a1d0eb8214f957c53f","sha256:8588e3be21fff843ba9e6f117a349e552efc8bf5121e173efd96460eceff41e6"],"state_sha256":"32952cd7f5fdaeecc5b229d9dff853298885df72479b111386b6ec04fb8db9c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oo9NiyPdWFNQ4Wx5G846ql+HtPt82gPKnc0SFoUlQN9TNGdILdqJBn7HOC8kc73/dMz57t+f2ch4f3oozHE6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T06:36:57.129730Z","bundle_sha256":"47b9adf3310b8913ae7e9e05c9153dc85985085f9085410f9ebd8e16b13014cd"}}