{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UT46OAW2I3CH7YB2C2DBJ4TCQY","short_pith_number":"pith:UT46OAW2","canonical_record":{"source":{"id":"1409.0143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-30T18:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"4d9e9878e47d5391d697df232f5c7c851bd75c87aa2bb88484a68eca48603ef0","abstract_canon_sha256":"c9aac3a54f60264b35c042cf21132f6a148a0cd504a71590d72fde859e92333e"},"schema_version":"1.0"},"canonical_sha256":"a4f9e702da46c47fe03a168614f262863334434906290baecac26fd2efb5eca2","source":{"kind":"arxiv","id":"1409.0143","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0143","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0143v3","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0143","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"UT46OAW2I3CH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UT46OAW2I3CH7YB2","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UT46OAW2","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UT46OAW2I3CH7YB2C2DBJ4TCQY","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-30T18:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"4d9e9878e47d5391d697df232f5c7c851bd75c87aa2bb88484a68eca48603ef0","abstract_canon_sha256":"c9aac3a54f60264b35c042cf21132f6a148a0cd504a71590d72fde859e92333e"},"schema_version":"1.0"},"canonical_sha256":"a4f9e702da46c47fe03a168614f262863334434906290baecac26fd2efb5eca2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:14.824519Z","signature_b64":"7VGjs6plmmJkbs8DoTgtLAnuCbn2sijWZ6YN9ZA7BoMadZKzHNmuNyAYZZQBYmgn9aLaiILpkjf9/t/vFoOrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4f9e702da46c47fe03a168614f262863334434906290baecac26fd2efb5eca2","last_reissued_at":"2026-05-18T01:28:14.823773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:14.823773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0143","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TQg+g0vDQQnfzAIjkvNuhe9tTZEoRwdY+7DIi7lCXJCnb3sPar/I6ASb8UpX3Z+KkB/zbtPDt30QTu12TmctBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:08:08.774401Z"},"content_sha256":"e97a68d0eb5eaa273115e7649c58d18c5863332fafbd1750ef47cc0a885fcf2c","schema_version":"1.0","event_id":"sha256:e97a68d0eb5eaa273115e7649c58d18c5863332fafbd1750ef47cc0a885fcf2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UT46OAW2I3CH7YB2C2DBJ4TCQY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radial Symmetry on 3D Shells in the Landau-de Gennes Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Apala Majumdar, Giacomo Canevari, Mythily Ramaswamy","submitted_at":"2014-08-30T18:35:06Z","abstract_excerpt":"We study the stability of the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We show that the radial-hedgehog solution has no zeroes for a sufficiently narrow shell, for all temperatures below the nematic supercooling temperature. We prove that the radial-hedgehog solution is the unique global Landau-de Gennes energy minimizer for a sufficiently narrow 3D spherical shell, for all temperatures below the nematic supercooling temperature. We provide explicit geometry-dependent cr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0143","kind":"arxiv","version":3},"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":"2026-05-18T01:28:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Fff/gnYsa4KL6jNB/9/usflB3wpWtVvEdO5LW7dq2fIOF+iLboWWZ7eQOZqyFm0+74b++1czFlAkyPWjm0ACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:08:08.774756Z"},"content_sha256":"701fe2b0aed84459d06ec8bc4d1756502c2e0a83036bf4e4e844d33b9eea9049","schema_version":"1.0","event_id":"sha256:701fe2b0aed84459d06ec8bc4d1756502c2e0a83036bf4e4e844d33b9eea9049"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY/bundle.json","state_url":"https://pith.science/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY/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":"2026-06-02T13:08:08Z","links":{"resolver":"https://pith.science/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY","bundle":"https://pith.science/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY/bundle.json","state":"https://pith.science/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UT46OAW2I3CH7YB2C2DBJ4TCQY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UT46OAW2I3CH7YB2C2DBJ4TCQY","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":"c9aac3a54f60264b35c042cf21132f6a148a0cd504a71590d72fde859e92333e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-30T18:35:06Z","title_canon_sha256":"4d9e9878e47d5391d697df232f5c7c851bd75c87aa2bb88484a68eca48603ef0"},"schema_version":"1.0","source":{"id":"1409.0143","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0143","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0143v3","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0143","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"UT46OAW2I3CH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UT46OAW2I3CH7YB2","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UT46OAW2","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:701fe2b0aed84459d06ec8bc4d1756502c2e0a83036bf4e4e844d33b9eea9049","target":"graph","created_at":"2026-05-18T01:28:14Z","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 the stability of the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We show that the radial-hedgehog solution has no zeroes for a sufficiently narrow shell, for all temperatures below the nematic supercooling temperature. We prove that the radial-hedgehog solution is the unique global Landau-de Gennes energy minimizer for a sufficiently narrow 3D spherical shell, for all temperatures below the nematic supercooling temperature. We provide explicit geometry-dependent cr","authors_text":"Apala Majumdar, Giacomo Canevari, Mythily Ramaswamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-30T18:35:06Z","title":"Radial Symmetry on 3D Shells in the Landau-de Gennes Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0143","kind":"arxiv","version":3},"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:e97a68d0eb5eaa273115e7649c58d18c5863332fafbd1750ef47cc0a885fcf2c","target":"record","created_at":"2026-05-18T01:28:14Z","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":"c9aac3a54f60264b35c042cf21132f6a148a0cd504a71590d72fde859e92333e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-30T18:35:06Z","title_canon_sha256":"4d9e9878e47d5391d697df232f5c7c851bd75c87aa2bb88484a68eca48603ef0"},"schema_version":"1.0","source":{"id":"1409.0143","kind":"arxiv","version":3}},"canonical_sha256":"a4f9e702da46c47fe03a168614f262863334434906290baecac26fd2efb5eca2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4f9e702da46c47fe03a168614f262863334434906290baecac26fd2efb5eca2","first_computed_at":"2026-05-18T01:28:14.823773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:14.823773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7VGjs6plmmJkbs8DoTgtLAnuCbn2sijWZ6YN9ZA7BoMadZKzHNmuNyAYZZQBYmgn9aLaiILpkjf9/t/vFoOrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:14.824519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0143","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e97a68d0eb5eaa273115e7649c58d18c5863332fafbd1750ef47cc0a885fcf2c","sha256:701fe2b0aed84459d06ec8bc4d1756502c2e0a83036bf4e4e844d33b9eea9049"],"state_sha256":"f8df7c10a6e3d104ab0c38dbf8a313a29807553b0ddb7fe9749b21bf9ec02bfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMWSUQ0p0tS4D3mQ7E+ObHZkHl7tOaAR8Fw0Ca8aBsNsM77TlBu1BUEx7T4Qj9SFa+uRguXnHUc4DiYIcXbPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:08:08.777237Z","bundle_sha256":"0cb385587edc485a015a1fbb87daf8ce6135847a85c650626c1d07b2def86400"}}