{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4CR4SC6OHDKTUG7AAPO2CJJIKV","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":"a6b3e72dbd13c6cb8f81835fdc09c31b8884347e48c2ebc3d8b53cd7629c590b","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.IV","submitted_at":"2021-02-19T17:22:16Z","title_canon_sha256":"e0c21539139a21c1958e432ab0dc07b08523c142c0def413b7fc47d5863d7555"},"schema_version":"1.0","source":{"id":"2102.10038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.10038","created_at":"2026-07-05T02:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"2102.10038v1","created_at":"2026-07-05T02:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.10038","created_at":"2026-07-05T02:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"4CR4SC6OHDKT","created_at":"2026-07-05T02:16:39Z"},{"alias_kind":"pith_short_16","alias_value":"4CR4SC6OHDKTUG7A","created_at":"2026-07-05T02:16:39Z"},{"alias_kind":"pith_short_8","alias_value":"4CR4SC6O","created_at":"2026-07-05T02:16:39Z"}],"graph_snapshots":[{"event_id":"sha256:c4b8c0547853d2aea15bde8e779df52baeab92decb2944f4696aab814c6523a0","target":"graph","created_at":"2026-07-05T02:16:39Z","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/2102.10038/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Integrating mathematical morphology operations within deep neural networks has been subject to increasing attention lately. However, replacing standard convolution layers with erosions or dilations is particularly challenging because the min and max operations are not differentiable. Relying on the asymptotic behavior of the counter-harmonic mean, p-convolutional layers were proposed as a possible workaround to this issue since they can perform pseudo-dilation or pseudo-erosion operations (depending on the value of their inner parameter p), and very promising results were reported. In this wor","authors_text":"Alexandre Kirszenberg, Elodie Puybareau, Guillaume Tochon, Jesus Angulo","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.IV","submitted_at":"2021-02-19T17:22:16Z","title":"Going beyond p-convolutions to learn grayscale morphological operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.10038","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":"sha256:2615b7dd264de6d545231c3531bedcf0d1f0f14aa1cd47ba1a06c012e5a0ea84","target":"record","created_at":"2026-07-05T02:16:39Z","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":"a6b3e72dbd13c6cb8f81835fdc09c31b8884347e48c2ebc3d8b53cd7629c590b","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.IV","submitted_at":"2021-02-19T17:22:16Z","title_canon_sha256":"e0c21539139a21c1958e432ab0dc07b08523c142c0def413b7fc47d5863d7555"},"schema_version":"1.0","source":{"id":"2102.10038","kind":"arxiv","version":1}},"canonical_sha256":"e0a3c90bce38d53a1be003dda1252855652eb509054b162b1213c872cf31c326","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0a3c90bce38d53a1be003dda1252855652eb509054b162b1213c872cf31c326","first_computed_at":"2026-07-05T02:16:39.051873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:16:39.051873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KN6Rve3VbQICLveFtH9WV6hYoAbFhnqwg1eQUL7N9kQp0YYeFxjUpnhHAWXQLT4UBegvbdFOIHwuu3YByzGCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:16:39.052195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.10038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2615b7dd264de6d545231c3531bedcf0d1f0f14aa1cd47ba1a06c012e5a0ea84","sha256:c4b8c0547853d2aea15bde8e779df52baeab92decb2944f4696aab814c6523a0"],"state_sha256":"b3fc95fc0f7a7217f4f9311814952e9e2584f5fbf7be790c39f3a6762f151eeb"}