{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QDXC2BDCOHYKR2PAYERFK4ZRKB","short_pith_number":"pith:QDXC2BDC","canonical_record":{"source":{"id":"2605.23603","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T13:12:04Z","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NE"],"title_canon_sha256":"e41ef585e2227b44f2586dcbd68a1a2e3046f77971fcfce01af21866879fc783","abstract_canon_sha256":"4b1499ac934b6066169915497903e873271aaec3ad08289593a23e31a9a55ca1"},"schema_version":"1.0"},"canonical_sha256":"80ee2d046271f0a8e9e0c122557331504ee393c99a0b506577b4ee729e4f478b","source":{"kind":"arxiv","id":"2605.23603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23603","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23603v1","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23603","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"QDXC2BDCOHYK","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"pith_short_16","alias_value":"QDXC2BDCOHYKR2PA","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"pith_short_8","alias_value":"QDXC2BDC","created_at":"2026-05-25T02:02:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QDXC2BDCOHYKR2PAYERFK4ZRKB","target":"record","payload":{"canonical_record":{"source":{"id":"2605.23603","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T13:12:04Z","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NE"],"title_canon_sha256":"e41ef585e2227b44f2586dcbd68a1a2e3046f77971fcfce01af21866879fc783","abstract_canon_sha256":"4b1499ac934b6066169915497903e873271aaec3ad08289593a23e31a9a55ca1"},"schema_version":"1.0"},"canonical_sha256":"80ee2d046271f0a8e9e0c122557331504ee393c99a0b506577b4ee729e4f478b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:21.729469Z","signature_b64":"wAnMjAXfEHt+2J1TAauGQXVNHL3G4D+FC1Gh+FfN4h1hWVwKZMH7oo2D/32zTvUzquRDJD2GK7R6JDPj8h3iDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80ee2d046271f0a8e9e0c122557331504ee393c99a0b506577b4ee729e4f478b","last_reissued_at":"2026-05-25T02:02:21.728635Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:21.728635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.23603","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pKyzqJiqTVaxJHxXTXmS2wXX19RQK4m0J4qxvGFqc+WEdJOojW6H0Q7+yy6Ez1FHuSJlmCGPnkGur426nXSRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:59.571488Z"},"content_sha256":"deb2405ff74861486cb19fc8d97027113124dd872473a7345de07f16ccb8cbf2","schema_version":"1.0","event_id":"sha256:deb2405ff74861486cb19fc8d97027113124dd872473a7345de07f16ccb8cbf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QDXC2BDCOHYKR2PAYERFK4ZRKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preisach Attention: A Hysteretic Model of Sequential Memory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI","cs.NE"],"primary_cat":"cs.LG","authors_text":"Piotr Frydrych","submitted_at":"2026-05-22T13:12:04Z","abstract_excerpt":"We introduce the Preisach Attention Layer (PAL), a novel sequence modelling architecture grounded in the classical Preisach hysteresis operator from mathematical physics. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and deactivation thresholds, maintaining a stack of local extrema as its internal state. A single-layer PAL-Transformer with O(1) depth is Turing-complete under arbitrary precision arithmetic, achievable through simulation of a two-stack pushdown automaton -- in contrast to the O(log n) depth required by standard hard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23603","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23603/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-25T02:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3UEDOnVJBaFCwFOR4xWHJnrICgd0xPZx7JtBm26GEyEW0TWVouZkWpOiLTKHfsWbOAj9LVrE5TrdEl5SM9y3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:59.572213Z"},"content_sha256":"4529cd576b12607bf45c650d8f8e5a55d75945130b6304dd7c006efb1af46c25","schema_version":"1.0","event_id":"sha256:4529cd576b12607bf45c650d8f8e5a55d75945130b6304dd7c006efb1af46c25"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:QDXC2BDCOHYKR2PAYERFK4ZRKB","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.3389/fphy.2014.00005.Isaak) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"doi: 10.3389/fphy. 2014.00005. Isaak D. Mayergoyz.Mathematical Models of Hysteresis. Springer, New York,","arxiv_id":"2605.23603","detector":"doi_compliance","evidence":{"ref_index":12,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"doi: 10.3389/fphy. 2014.00005. Isaak D. Mayergoyz.Mathematical Models of Hysteresis. Springer, New York,","reconstructed_doi":"10.3389/fphy.2014.00005.Isaak"},"severity":"advisory","ref_index":12,"audited_at":"2026-05-25T04:48:07.500345Z","event_type":"pith.integrity.v1","detected_doi":"10.3389/fphy.2014.00005.Isaak","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"98a6e31a14a411de85950466e55e5613fd3fc79b203127d4ff6196d52e5f827f","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7361,"payload_sha256":"5efe3708979aadc82327bc245f1f2f1ca799c1dea05c15ffc7ae4b546070a313","signature_b64":"DOvoHfH6FfzVQZVsy8u/z4AReVsIeqMSrn1tT36nYoiPlARcJQfnLokKIDU/5cqZetb2iJVenhP4C0ugIgpHBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T04:49:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ijWoD2H+bwMweYbkvrEkzMVkODN60mhKIKUznZlNgCgS5CtPPqVJ9sydvLV1EpY7faM1m0QgNCrm1bjlfwrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:54:59.573588Z"},"content_sha256":"63f769d16b885e14167a2900f733959939687edda56739e663bf93edb4f4cdb1","schema_version":"1.0","event_id":"sha256:63f769d16b885e14167a2900f733959939687edda56739e663bf93edb4f4cdb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB/bundle.json","state_url":"https://pith.science/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB/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":"2026-05-26T21:54:59Z","links":{"resolver":"https://pith.science/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB","bundle":"https://pith.science/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB/bundle.json","state":"https://pith.science/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDXC2BDCOHYKR2PAYERFK4ZRKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QDXC2BDCOHYKR2PAYERFK4ZRKB","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4b1499ac934b6066169915497903e873271aaec3ad08289593a23e31a9a55ca1","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T13:12:04Z","title_canon_sha256":"e41ef585e2227b44f2586dcbd68a1a2e3046f77971fcfce01af21866879fc783"},"schema_version":"1.0","source":{"id":"2605.23603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23603","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23603v1","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23603","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"QDXC2BDCOHYK","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"pith_short_16","alias_value":"QDXC2BDCOHYKR2PA","created_at":"2026-05-25T02:02:21Z"},{"alias_kind":"pith_short_8","alias_value":"QDXC2BDC","created_at":"2026-05-25T02:02:21Z"}],"graph_snapshots":[{"event_id":"sha256:4529cd576b12607bf45c650d8f8e5a55d75945130b6304dd7c006efb1af46c25","target":"graph","created_at":"2026-05-25T02:02:21Z","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/2605.23603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the Preisach Attention Layer (PAL), a novel sequence modelling architecture grounded in the classical Preisach hysteresis operator from mathematical physics. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and deactivation thresholds, maintaining a stack of local extrema as its internal state. A single-layer PAL-Transformer with O(1) depth is Turing-complete under arbitrary precision arithmetic, achievable through simulation of a two-stack pushdown automaton -- in contrast to the O(log n) depth required by standard hard","authors_text":"Piotr Frydrych","cross_cats":["cond-mat.dis-nn","cs.AI","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T13:12:04Z","title":"Preisach Attention: A Hysteretic Model of Sequential Memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23603","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:deb2405ff74861486cb19fc8d97027113124dd872473a7345de07f16ccb8cbf2","target":"record","created_at":"2026-05-25T02:02:21Z","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":"4b1499ac934b6066169915497903e873271aaec3ad08289593a23e31a9a55ca1","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-22T13:12:04Z","title_canon_sha256":"e41ef585e2227b44f2586dcbd68a1a2e3046f77971fcfce01af21866879fc783"},"schema_version":"1.0","source":{"id":"2605.23603","kind":"arxiv","version":1}},"canonical_sha256":"80ee2d046271f0a8e9e0c122557331504ee393c99a0b506577b4ee729e4f478b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80ee2d046271f0a8e9e0c122557331504ee393c99a0b506577b4ee729e4f478b","first_computed_at":"2026-05-25T02:02:21.728635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:21.728635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wAnMjAXfEHt+2J1TAauGQXVNHL3G4D+FC1Gh+FfN4h1hWVwKZMH7oo2D/32zTvUzquRDJD2GK7R6JDPj8h3iDg==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:21.729469Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:deb2405ff74861486cb19fc8d97027113124dd872473a7345de07f16ccb8cbf2","sha256:4529cd576b12607bf45c650d8f8e5a55d75945130b6304dd7c006efb1af46c25","sha256:63f769d16b885e14167a2900f733959939687edda56739e663bf93edb4f4cdb1"],"state_sha256":"7dff45a1040403d7390678e4d0f2f52ad4f03b41308ac0701559f4f8b4da5af0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xzm7Qx6U++SQJlwGWOu0ER2CqLo6bD+BTygCF3XBTifVAXowPSb3JPJjlvIekm0u/4XrduFCag0LTLBtX09Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:54:59.576279Z","bundle_sha256":"7ca1142832a80dae0a76707e0db3973c0b6dcb9f444b77355f6a9c8f8b6026ac"}}