{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KNRIQHIHLBR3A6WGYQYY6MYKHD","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":"cd6615b0c19b7fd65242cc9afdf88cf205b12b200e78be7f584bf6b3f13fc301","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T13:08:23Z","title_canon_sha256":"890bd8885aff5746ecce34b165a8529ac27c84335a7eff647869147e47c50a58"},"schema_version":"1.0","source":{"id":"2606.10824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10824","created_at":"2026-06-10T01:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10824v1","created_at":"2026-06-10T01:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10824","created_at":"2026-06-10T01:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"KNRIQHIHLBR3","created_at":"2026-06-10T01:10:42Z"},{"alias_kind":"pith_short_16","alias_value":"KNRIQHIHLBR3A6WG","created_at":"2026-06-10T01:10:42Z"},{"alias_kind":"pith_short_8","alias_value":"KNRIQHIH","created_at":"2026-06-10T01:10:42Z"}],"graph_snapshots":[{"event_id":"sha256:56745d0792769af0c2079a967b2aa3f00562eb8cbcbc352eca4d7dcee8a08eff","target":"graph","created_at":"2026-06-10T01:10:42Z","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/2606.10824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Characteristic Transform (ECT) is the injective shape descriptor obtained by collecting ECCs over many directions. How the ECT is encoded for a neural network is itself an inductive bias, conventionally fixed by discretizing each ECC. We introduce a continuous encoding: for each direction and each vertex it records the net Euler-characteristic change attributed to that vertex, producing a per-direction token sequence th","authors_text":"Bastian Rieck, Elena Xinyi Wang, Lars M. Salbu, Nello Blaser, Odin Hoff Gardaa","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T13:08:23Z","title":"Encoding the Euler Characteristic Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10824","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":"sha256:831a5d50ed55da454c015b08b08074f9d7bc9be1bd0f98c6eaccbc84641cd9ff","target":"record","created_at":"2026-06-10T01:10:42Z","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":"cd6615b0c19b7fd65242cc9afdf88cf205b12b200e78be7f584bf6b3f13fc301","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-09T13:08:23Z","title_canon_sha256":"890bd8885aff5746ecce34b165a8529ac27c84335a7eff647869147e47c50a58"},"schema_version":"1.0","source":{"id":"2606.10824","kind":"arxiv","version":1}},"canonical_sha256":"5362881d075863b07ac6c4318f330a38ce87513f79b850f9946cfc6374dd680b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5362881d075863b07ac6c4318f330a38ce87513f79b850f9946cfc6374dd680b","first_computed_at":"2026-06-10T01:10:42.544788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:42.544788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1XTK37gGfZMd4jGxYzsUuTuSIMIww+J9jwSqH1snUq6eYfpW5NscmyGEdKbLXu46MmYP/ZoxYzByWH0avgMbAg==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:42.545635Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:831a5d50ed55da454c015b08b08074f9d7bc9be1bd0f98c6eaccbc84641cd9ff","sha256:56745d0792769af0c2079a967b2aa3f00562eb8cbcbc352eca4d7dcee8a08eff"],"state_sha256":"4aa9afedde48a9f90ea72901a6115b698631850ecdfffe9eecc1e893451847be"}