{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3B354H4DJGN3ALESGUM6GHJKP7","short_pith_number":"pith:3B354H4D","canonical_record":{"source":{"id":"1108.1573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-08-07T21:14:49Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7ad7c472a7baf00ccc56f89e4bec06a4f350ff87f4be4f98d42af7852a065df1","abstract_canon_sha256":"f6222113e49307d0d7efb653134e1986d388b2aaa030cc9228a567f6c4840e83"},"schema_version":"1.0"},"canonical_sha256":"d877de1f83499bb02c923519e31d2a7fc0f78f253a1d6a2160208c4e0bcc40c6","source":{"kind":"arxiv","id":"1108.1573","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1573","created_at":"2026-05-18T02:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1573v1","created_at":"2026-05-18T02:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1573","created_at":"2026-05-18T02:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"3B354H4DJGN3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3B354H4DJGN3ALES","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3B354H4D","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3B354H4DJGN3ALESGUM6GHJKP7","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-08-07T21:14:49Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7ad7c472a7baf00ccc56f89e4bec06a4f350ff87f4be4f98d42af7852a065df1","abstract_canon_sha256":"f6222113e49307d0d7efb653134e1986d388b2aaa030cc9228a567f6c4840e83"},"schema_version":"1.0"},"canonical_sha256":"d877de1f83499bb02c923519e31d2a7fc0f78f253a1d6a2160208c4e0bcc40c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:00.614280Z","signature_b64":"okSbhBrmT0w0BfffFcj5lPlA2PnqbQIl+tKNV8qDGNHlqN3Ok/rAsSPOQHnY85Ix0drU//0pNJRRR85CTTfxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d877de1f83499bb02c923519e31d2a7fc0f78f253a1d6a2160208c4e0bcc40c6","last_reissued_at":"2026-05-18T02:01:00.613595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:00.613595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1573","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":"2026-05-18T02:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75DWxIaX1gEWmwHE3pFXDyUqsuP3VvWBmkevtl6jvDAIN07dFXRGDOvvfW/h45+unQL0oN6cD7WpQb35GSGWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:15:18.596765Z"},"content_sha256":"33479f7e47abfd95d34579dbfad13a369dd1cb9cd56ba7ed49baeae9b5b26b0d","schema_version":"1.0","event_id":"sha256:33479f7e47abfd95d34579dbfad13a369dd1cb9cd56ba7ed49baeae9b5b26b0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3B354H4DJGN3ALESGUM6GHJKP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Frustrated order on extrinsic geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Badel L. Mbanga, Christian D. Santangelo, Gregory M. Grason","submitted_at":"2011-08-07T21:14:49Z","abstract_excerpt":"We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable and most important on surfaces of negative Gaussian curvature, where it leads to a complex ground state thermodynamics. We show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1573","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":"2026-05-18T02:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgcGJSXh+guQeOKj88DMsj+tlO+ac/+OhybxcvJJgLOdkCVxd7L3ApqMUDd4iKZioeYuZxSp75nqBrsKXRWMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:15:18.597527Z"},"content_sha256":"2686ede34c2fd10dbfe7c96bf4c5b1c5a8877669477654221d3d88b4f350f61f","schema_version":"1.0","event_id":"sha256:2686ede34c2fd10dbfe7c96bf4c5b1c5a8877669477654221d3d88b4f350f61f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3B354H4DJGN3ALESGUM6GHJKP7/bundle.json","state_url":"https://pith.science/pith/3B354H4DJGN3ALESGUM6GHJKP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3B354H4DJGN3ALESGUM6GHJKP7/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":"2026-06-10T11:15:18Z","links":{"resolver":"https://pith.science/pith/3B354H4DJGN3ALESGUM6GHJKP7","bundle":"https://pith.science/pith/3B354H4DJGN3ALESGUM6GHJKP7/bundle.json","state":"https://pith.science/pith/3B354H4DJGN3ALESGUM6GHJKP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3B354H4DJGN3ALESGUM6GHJKP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3B354H4DJGN3ALESGUM6GHJKP7","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":"f6222113e49307d0d7efb653134e1986d388b2aaa030cc9228a567f6c4840e83","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-08-07T21:14:49Z","title_canon_sha256":"7ad7c472a7baf00ccc56f89e4bec06a4f350ff87f4be4f98d42af7852a065df1"},"schema_version":"1.0","source":{"id":"1108.1573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1573","created_at":"2026-05-18T02:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1573v1","created_at":"2026-05-18T02:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1573","created_at":"2026-05-18T02:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"3B354H4DJGN3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3B354H4DJGN3ALES","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3B354H4D","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:2686ede34c2fd10dbfe7c96bf4c5b1c5a8877669477654221d3d88b4f350f61f","target":"graph","created_at":"2026-05-18T02:01:00Z","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":"We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable and most important on surfaces of negative Gaussian curvature, where it leads to a complex ground state thermodynamics. We show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic ","authors_text":"Badel L. Mbanga, Christian D. Santangelo, Gregory M. Grason","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-08-07T21:14:49Z","title":"Frustrated order on extrinsic geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1573","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":"sha256:33479f7e47abfd95d34579dbfad13a369dd1cb9cd56ba7ed49baeae9b5b26b0d","target":"record","created_at":"2026-05-18T02:01:00Z","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":"f6222113e49307d0d7efb653134e1986d388b2aaa030cc9228a567f6c4840e83","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-08-07T21:14:49Z","title_canon_sha256":"7ad7c472a7baf00ccc56f89e4bec06a4f350ff87f4be4f98d42af7852a065df1"},"schema_version":"1.0","source":{"id":"1108.1573","kind":"arxiv","version":1}},"canonical_sha256":"d877de1f83499bb02c923519e31d2a7fc0f78f253a1d6a2160208c4e0bcc40c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d877de1f83499bb02c923519e31d2a7fc0f78f253a1d6a2160208c4e0bcc40c6","first_computed_at":"2026-05-18T02:01:00.613595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:00.613595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"okSbhBrmT0w0BfffFcj5lPlA2PnqbQIl+tKNV8qDGNHlqN3Ok/rAsSPOQHnY85Ix0drU//0pNJRRR85CTTfxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:00.614280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33479f7e47abfd95d34579dbfad13a369dd1cb9cd56ba7ed49baeae9b5b26b0d","sha256:2686ede34c2fd10dbfe7c96bf4c5b1c5a8877669477654221d3d88b4f350f61f"],"state_sha256":"eeba9bcf8d4974cc54708475c427d5bb8e327fc6a1bfa0e81baca9de27a62be7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+9W2TF7wfFn9mZd5v8QwP+62FkWNgPwUzbkIZ3fTEJ3uQWzt8nwTd7u+OQ00LlLvahUpJpV9JnH3uhWjTHjBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:15:18.601836Z","bundle_sha256":"c1c8758668cf5c64a7d0f1811b1805bc9d6b73fe7508de30f2bf63d436a85562"}}