{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EOE35EL3LSKUTIFKKBJ72R2RE4","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":"a6c1e8e3b6a3c54899ac5a96ddc1053a32b182b8080923e0e1eeb7ee2bce4a57","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2026-07-28T15:22:37Z","title_canon_sha256":"c4670b06950ea165de92287cccf7cb372e8607b7dffb22610ebe7d363b32fed9"},"schema_version":"1.0","source":{"id":"2607.25848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25848","created_at":"2026-07-29T01:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25848v1","created_at":"2026-07-29T01:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25848","created_at":"2026-07-29T01:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"EOE35EL3LSKU","created_at":"2026-07-29T01:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EOE35EL3LSKUTIFK","created_at":"2026-07-29T01:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EOE35EL3","created_at":"2026-07-29T01:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:83426671cc7d06ec98b02fdcc3ba78f14f2caa7b10daf5d83c96b60df97816f1","target":"graph","created_at":"2026-07-29T01:26:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.25848/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Topological classification of physical vector fields conventionally relies on field normalization and homotopy-based invariants. However, when field amplitudes vanish, normalization becomes ill-defined, preventing a direct topological characterization. Here, we introduce a general framework for the topological classification of non-normalizable $n$-dimensional vector fields with compactifiable base spaces by transforming them into $(n+1)$-dimensional normalized vector fields. This construction extends homotopy-based classification to fields containing amplitude zeros. We explicitly demonstrate","authors_text":"Alessandro Pignedoli, Alexander Neuhaus, Frank-J. Meyer zu Heringdorf, Karin Everschor-Sitte, Maria Azhar, Philipp Gessler","cross_cats":["cond-mat.soft","math-ph","math.MP","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2026-07-28T15:22:37Z","title":"Topological Classification of Non-Normalizable Vector Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25848","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":"sha256:2b0c21068a2de30e7c0a6ab964ed8a43c7bf1da2d3e8127ea67d602f34746695","target":"record","created_at":"2026-07-29T01:26:06Z","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":"a6c1e8e3b6a3c54899ac5a96ddc1053a32b182b8080923e0e1eeb7ee2bce4a57","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2026-07-28T15:22:37Z","title_canon_sha256":"c4670b06950ea165de92287cccf7cb372e8607b7dffb22610ebe7d363b32fed9"},"schema_version":"1.0","source":{"id":"2607.25848","kind":"arxiv","version":1}},"canonical_sha256":"2389be917b5c9549a0aa5053fd47512733b5274faaa7dd8648cb37b8bf30f947","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2389be917b5c9549a0aa5053fd47512733b5274faaa7dd8648cb37b8bf30f947","first_computed_at":"2026-07-29T01:26:06.429848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T01:26:06.429848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nFM4+guk3c5v4xEUUlgI5JnpD/vVdcKp9oOg8dF0R+2XspsV/H8/Ls5cXydB2YFa11qXxNRLGulVVFQm2rEGBQ==","signature_status":"signed_v1","signed_at":"2026-07-29T01:26:06.430765Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b0c21068a2de30e7c0a6ab964ed8a43c7bf1da2d3e8127ea67d602f34746695","sha256:83426671cc7d06ec98b02fdcc3ba78f14f2caa7b10daf5d83c96b60df97816f1"],"state_sha256":"bd7d681a00dcc017988af3727b28c1577221e6c017f99cb92c3dd8f91c9177b6"}