{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UAPV3H4WU5LFFDK2B3QQIKNTVH","short_pith_number":"pith:UAPV3H4W","canonical_record":{"source":{"id":"2606.24961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-23T09:08:15Z","cross_cats_sorted":["physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"905a3877d8337186fdb0a715df3e6d3c86931a7634c0e0245d9518ea7315e3ff","abstract_canon_sha256":"e32087f00ceee06ed7f480eac7e2e9e6dc7ecd93bbc938048449b42268aa64a3"},"schema_version":"1.0"},"canonical_sha256":"a01f5d9f96a756528d5a0ee10429b3a9ca07c4d97cf18974f7ec477ed0f9a1c4","source":{"kind":"arxiv","id":"2606.24961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24961","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24961v1","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24961","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"UAPV3H4WU5LF","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAPV3H4WU5LFFDK2","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAPV3H4W","created_at":"2026-06-25T00:17:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UAPV3H4WU5LFFDK2B3QQIKNTVH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-23T09:08:15Z","cross_cats_sorted":["physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"905a3877d8337186fdb0a715df3e6d3c86931a7634c0e0245d9518ea7315e3ff","abstract_canon_sha256":"e32087f00ceee06ed7f480eac7e2e9e6dc7ecd93bbc938048449b42268aa64a3"},"schema_version":"1.0"},"canonical_sha256":"a01f5d9f96a756528d5a0ee10429b3a9ca07c4d97cf18974f7ec477ed0f9a1c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T00:17:46.979257Z","signature_b64":"S+sE7q+m3Gg7VwMVD6KKNxrFo/8rXjrGNuXvMy2rRP/5omw/wNev3LfERnW874JdupHv7gzZISW/mTc8aYCeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a01f5d9f96a756528d5a0ee10429b3a9ca07c4d97cf18974f7ec477ed0f9a1c4","last_reissued_at":"2026-06-25T00:17:46.978843Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T00:17:46.978843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24961","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":"2026-06-25T00:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JNv0SjjdZR+OeQvHJqGk6xOwQaPCFQ2b9vtt6C17G4r9prgZ60FQpRcuvWrx++EMFYQLNne00OQUm4Wt25omBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:46:24.313099Z"},"content_sha256":"67883f1622d9cc493b4a03b023ac2ff46e6ab7acf5558d1088d4d66239a0ae30","schema_version":"1.0","event_id":"sha256:67883f1622d9cc493b4a03b023ac2ff46e6ab7acf5558d1088d4d66239a0ae30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UAPV3H4WU5LFFDK2B3QQIKNTVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature-induced smectic-C order of tangentially anchored hard spherocylinders on a sphere with a rigidly locked director field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph","physics.comp-ph"],"primary_cat":"cond-mat.soft","authors_text":"Elshad Allahyarov, Hartmut L\\\"owen, Jonathan Washburn","submitted_at":"2026-06-23T09:08:15Z","abstract_excerpt":"We study the strict locked-orientation limit of hard spherocylinders on a sphere, in which the rod axes are rigidly locked to a prescribed tangential director field and cannot reorient. Because the bulk hard-rod phase diagram contains no smectic-C phase, any coherent tilt isolates a geometric curvature mechanism rather than a finite-stiffness equilibrium effect. A ratio-symmetric recognition cost fixes the layer spacing at the bulk close-contact value and yields a hierarchy of geometric statements: the lower edge of the smectic-area window at $45^\\circ$ follows from reciprocal symmetry; the up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24961","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-25T00:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rpGJXwG5ZKaIds3/WxJ08pEm1zHrc1ScgdW6wIK5W9A+j0z4TMBaA0RUqgK2UGNsirvYmX5AogjNweMIi5v0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:46:24.313497Z"},"content_sha256":"eac8adbffded3f25a98e4f186eefba485692e074b17eb7d405d5c93e842d174a","schema_version":"1.0","event_id":"sha256:eac8adbffded3f25a98e4f186eefba485692e074b17eb7d405d5c93e842d174a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH/bundle.json","state_url":"https://pith.science/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH/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":"2026-06-29T12:46:24Z","links":{"resolver":"https://pith.science/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH","bundle":"https://pith.science/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH/bundle.json","state":"https://pith.science/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAPV3H4WU5LFFDK2B3QQIKNTVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UAPV3H4WU5LFFDK2B3QQIKNTVH","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":"e32087f00ceee06ed7f480eac7e2e9e6dc7ecd93bbc938048449b42268aa64a3","cross_cats_sorted":["physics.chem-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-23T09:08:15Z","title_canon_sha256":"905a3877d8337186fdb0a715df3e6d3c86931a7634c0e0245d9518ea7315e3ff"},"schema_version":"1.0","source":{"id":"2606.24961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24961","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24961v1","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24961","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"UAPV3H4WU5LF","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"UAPV3H4WU5LFFDK2","created_at":"2026-06-25T00:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"UAPV3H4W","created_at":"2026-06-25T00:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:eac8adbffded3f25a98e4f186eefba485692e074b17eb7d405d5c93e842d174a","target":"graph","created_at":"2026-06-25T00:17:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.24961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the strict locked-orientation limit of hard spherocylinders on a sphere, in which the rod axes are rigidly locked to a prescribed tangential director field and cannot reorient. Because the bulk hard-rod phase diagram contains no smectic-C phase, any coherent tilt isolates a geometric curvature mechanism rather than a finite-stiffness equilibrium effect. A ratio-symmetric recognition cost fixes the layer spacing at the bulk close-contact value and yields a hierarchy of geometric statements: the lower edge of the smectic-area window at $45^\\circ$ follows from reciprocal symmetry; the up","authors_text":"Elshad Allahyarov, Hartmut L\\\"owen, Jonathan Washburn","cross_cats":["physics.chem-ph","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-23T09:08:15Z","title":"Curvature-induced smectic-C order of tangentially anchored hard spherocylinders on a sphere with a rigidly locked director field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24961","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":"sha256:67883f1622d9cc493b4a03b023ac2ff46e6ab7acf5558d1088d4d66239a0ae30","target":"record","created_at":"2026-06-25T00:17:46Z","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":"e32087f00ceee06ed7f480eac7e2e9e6dc7ecd93bbc938048449b42268aa64a3","cross_cats_sorted":["physics.chem-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-06-23T09:08:15Z","title_canon_sha256":"905a3877d8337186fdb0a715df3e6d3c86931a7634c0e0245d9518ea7315e3ff"},"schema_version":"1.0","source":{"id":"2606.24961","kind":"arxiv","version":1}},"canonical_sha256":"a01f5d9f96a756528d5a0ee10429b3a9ca07c4d97cf18974f7ec477ed0f9a1c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a01f5d9f96a756528d5a0ee10429b3a9ca07c4d97cf18974f7ec477ed0f9a1c4","first_computed_at":"2026-06-25T00:17:46.978843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T00:17:46.978843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S+sE7q+m3Gg7VwMVD6KKNxrFo/8rXjrGNuXvMy2rRP/5omw/wNev3LfERnW874JdupHv7gzZISW/mTc8aYCeBQ==","signature_status":"signed_v1","signed_at":"2026-06-25T00:17:46.979257Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67883f1622d9cc493b4a03b023ac2ff46e6ab7acf5558d1088d4d66239a0ae30","sha256:eac8adbffded3f25a98e4f186eefba485692e074b17eb7d405d5c93e842d174a"],"state_sha256":"57551e0ccb3dd038ff5d303261724077663241856a349d598fa9e99ae7f15585"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pz8IppbgtlVOkA6+2uRfx+eiRmaFKkQnDBN5p8zIqjtk7gP8/GimZW0nAC+rH+g+AleKT0Pmh6lDU7UhjR4UAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:46:24.315545Z","bundle_sha256":"74491caf8610ec7a56150c847c63c053e54adb5700003c6eff824dd39f2f90da"}}