{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KQSKUT4YPC4EDNIJX26SY5HRZZ","short_pith_number":"pith:KQSKUT4Y","canonical_record":{"source":{"id":"1611.08961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T02:15:32Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math.DG","math.MP"],"title_canon_sha256":"ee50e2ea3a4dd101694f69f3abbc30e863426819bd39e5ca3df261c4d3b303e5","abstract_canon_sha256":"0222f40fe14b09c136a4168a0aa555bbc2e4cd7fb1b3f74f4996c642691e03c8"},"schema_version":"1.0"},"canonical_sha256":"5424aa4f9878b841b509bebd2c74f1ce692a1ae9577079177e51c200aeec3987","source":{"kind":"arxiv","id":"1611.08961","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08961","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08961v3","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08961","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"KQSKUT4YPC4E","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQSKUT4YPC4EDNIJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQSKUT4Y","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KQSKUT4YPC4EDNIJX26SY5HRZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T02:15:32Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math.DG","math.MP"],"title_canon_sha256":"ee50e2ea3a4dd101694f69f3abbc30e863426819bd39e5ca3df261c4d3b303e5","abstract_canon_sha256":"0222f40fe14b09c136a4168a0aa555bbc2e4cd7fb1b3f74f4996c642691e03c8"},"schema_version":"1.0"},"canonical_sha256":"5424aa4f9878b841b509bebd2c74f1ce692a1ae9577079177e51c200aeec3987","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:06.914553Z","signature_b64":"fQU8qIValoZrE76BxHW/c080i2wEnzyak9oILhbXAdSf6nA/09iSK4UZDKAY8edtpa2iJb2IxSy7CaGcvhL2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5424aa4f9878b841b509bebd2c74f1ce692a1ae9577079177e51c200aeec3987","last_reissued_at":"2026-05-18T00:39:06.913907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:06.913907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08961","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":"2026-05-18T00:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2LHgpj4SXpwxTpLILWMWjpQmzo4CcAfj4HtSDmAv2vv5Zj29pYVURrcMO5f5M9IUgXFwno+tgUyjCGMtGZogCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:35:25.264725Z"},"content_sha256":"24b2d75b669ff07227564d85a317d8076d1b854f577e859d2a25cab057b4b33b","schema_version":"1.0","event_id":"sha256:24b2d75b669ff07227564d85a317d8076d1b854f577e859d2a25cab057b4b33b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KQSKUT4YPC4EDNIJX26SY5HRZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential topology of semimetals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Guo Chuan Thiang, Varghese Mathai","submitted_at":"2016-11-28T02:15:32Z","abstract_excerpt":"The subtle interplay between local and global charges for topological semimetals exactly parallels that for singular vector fields. Part of this story is the relationship between cohomological semimetal invariants, Euler structures, and ambiguities in the torsion of manifolds. Dually, a topological semimetal can be represented by Euler chains from which its surface Fermi arc connectivity can be deduced. These dual pictures, and the link to topological invariants of insulators, are organised using geometric exact sequences. We go beyond Dirac-type Hamiltonians and introduce new classes of semim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08961","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":"2026-05-18T00:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPvBmjClQH34/LS/Dx7AEeUWOUemdg/tx/PErqyfVFzuH3xuTRzlAaH3WXktQDumue4pT4M2Fvs3DJXsNje7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:35:25.265069Z"},"content_sha256":"fc864664eee4583b45d7b3c40fcee45c3990198243fbf64fa7af77a84888cd68","schema_version":"1.0","event_id":"sha256:fc864664eee4583b45d7b3c40fcee45c3990198243fbf64fa7af77a84888cd68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ/bundle.json","state_url":"https://pith.science/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ/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":"2026-06-05T06:35:25Z","links":{"resolver":"https://pith.science/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ","bundle":"https://pith.science/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ/bundle.json","state":"https://pith.science/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQSKUT4YPC4EDNIJX26SY5HRZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KQSKUT4YPC4EDNIJX26SY5HRZZ","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":"0222f40fe14b09c136a4168a0aa555bbc2e4cd7fb1b3f74f4996c642691e03c8","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T02:15:32Z","title_canon_sha256":"ee50e2ea3a4dd101694f69f3abbc30e863426819bd39e5ca3df261c4d3b303e5"},"schema_version":"1.0","source":{"id":"1611.08961","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08961","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08961v3","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08961","created_at":"2026-05-18T00:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"KQSKUT4YPC4E","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQSKUT4YPC4EDNIJ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQSKUT4Y","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:fc864664eee4583b45d7b3c40fcee45c3990198243fbf64fa7af77a84888cd68","target":"graph","created_at":"2026-05-18T00:39:06Z","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 subtle interplay between local and global charges for topological semimetals exactly parallels that for singular vector fields. Part of this story is the relationship between cohomological semimetal invariants, Euler structures, and ambiguities in the torsion of manifolds. Dually, a topological semimetal can be represented by Euler chains from which its surface Fermi arc connectivity can be deduced. These dual pictures, and the link to topological invariants of insulators, are organised using geometric exact sequences. We go beyond Dirac-type Hamiltonians and introduce new classes of semim","authors_text":"Guo Chuan Thiang, Varghese Mathai","cross_cats":["cond-mat.mes-hall","hep-th","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T02:15:32Z","title":"Differential topology of semimetals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08961","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":"sha256:24b2d75b669ff07227564d85a317d8076d1b854f577e859d2a25cab057b4b33b","target":"record","created_at":"2026-05-18T00:39:06Z","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":"0222f40fe14b09c136a4168a0aa555bbc2e4cd7fb1b3f74f4996c642691e03c8","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T02:15:32Z","title_canon_sha256":"ee50e2ea3a4dd101694f69f3abbc30e863426819bd39e5ca3df261c4d3b303e5"},"schema_version":"1.0","source":{"id":"1611.08961","kind":"arxiv","version":3}},"canonical_sha256":"5424aa4f9878b841b509bebd2c74f1ce692a1ae9577079177e51c200aeec3987","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5424aa4f9878b841b509bebd2c74f1ce692a1ae9577079177e51c200aeec3987","first_computed_at":"2026-05-18T00:39:06.913907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:06.913907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQU8qIValoZrE76BxHW/c080i2wEnzyak9oILhbXAdSf6nA/09iSK4UZDKAY8edtpa2iJb2IxSy7CaGcvhL2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:06.914553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08961","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24b2d75b669ff07227564d85a317d8076d1b854f577e859d2a25cab057b4b33b","sha256:fc864664eee4583b45d7b3c40fcee45c3990198243fbf64fa7af77a84888cd68"],"state_sha256":"48e82034b9aaeb969e9fe73c645c6a81852e00609848b6133088197a23adb1c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HE5KoBcIpsXvrfl4zz8jXPzXHdlFxX7jzXK+PAEugMvnkVBxlr/XA6QKFd75G8y4qrtnCYgZOWRYQjgD8bahCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:35:25.267078Z","bundle_sha256":"dcae0fe180da558b1181288457d36bf3492bdf39147810c638dfba545a60a3f2"}}