{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","short_pith_number":"pith:P64LSTQD","canonical_record":{"source":{"id":"2605.22644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"5aa39333e0097b93ef5577f5d61f8beb309f0718bb37441e8ea24c6114e3911a","abstract_canon_sha256":"86358fed8f0b2c5b763c46a67567acd2db7861d37ea499e960bd86a0f3814076"},"schema_version":"1.0"},"canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","source":{"kind":"arxiv","id":"2605.22644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22644","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22644v1","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22644","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"P64LSTQD5GRW","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"P64LSTQD5GRW6FSB","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"P64LSTQD","created_at":"2026-05-22T02:04:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"5aa39333e0097b93ef5577f5d61f8beb309f0718bb37441e8ea24c6114e3911a","abstract_canon_sha256":"86358fed8f0b2c5b763c46a67567acd2db7861d37ea499e960bd86a0f3814076"},"schema_version":"1.0"},"canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:47.754876Z","signature_b64":"cVao27D8qov53dxfL6iLwJgcdMkl4pjsV5Q+JvK1DiCN2kZF4ymssvUVtiPYg+yypP79LafNmMwbjCpJdXVZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","last_reissued_at":"2026-05-22T02:04:47.754035Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:47.754035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22644","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":"2026-05-22T02:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcVs1K17rw/2eLMTLN7nJebXi5lMAhxfTUVX4WFDD/YXIFw0VoytFP2xdMOkWULuFshx4mAvZld635iLM5dhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.347065Z"},"content_sha256":"fe796f1e00f070f18bd74b3f40f98517928581d251121e93caaaa4200703be30","schema_version":"1.0","event_id":"sha256:fe796f1e00f070f18bd74b3f40f98517928581d251121e93caaaa4200703be30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aleksandr Beznosikov, Aleksandr Kovalenko, Aleksandr Shestakov, Andrew Semenov, Andrey Leonidov, Andrey Veprikov, Anna Radovskaya, Egor Lopatin, Igor Ignashin, Stanislav Potapov","submitted_at":"2026-05-21T15:50:40Z","abstract_excerpt":"Stochastic Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion. However, this approximation relies on a continuous-time limit and a sqrt(eta) noise scaling that does not match the discrete SGD update at finite learning rate. In this work, we propose an alternative formulation of SGD as deterministic dynamics in a fluctuating loss landscape induced by minibatch sampling. Starting directly from the discrete update, we derive a master equation for the parameter distribution and obtain a discrete Fokker--Planck equation that diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22644","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/2605.22644/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":"2026-05-22T02:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YopSMfVfhLAaOLglXFq4LamH8WhQR+i2NXLfk7lnftwIeqhVvBQTewW0ySXPe2oz10oodEA6ySpndc9GALQrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.347511Z"},"content_sha256":"48d38dca88793d03e3d0ce638b9111a0cb819463557ad30b6181e17b7033eea9","schema_version":"1.0","event_id":"sha256:48d38dca88793d03e3d0ce638b9111a0cb819463557ad30b6181e17b7033eea9"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://link.aps' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://link.aps","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779665745.4073813},"severity":"advisory","ref_index":null,"audited_at":"2026-05-24T23:35:46.142622Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://link.aps","finding_type":"dead_url","evidence_hash":"190c89ed624d915fd795cd2a8cae503c63d6d6b5a76a2a090c82dec16c9cf5bd","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7214,"payload_sha256":"3389375786f88d1caf8c84a33cc78f7f1f856569a14834f236406ceb851b6b48","signature_b64":"oFoDtIbu36OYjW4NlNO/L9qcAk3225T1y78rh/fcBydpHh4hIokJ3ecjaduLugecBOQN7qcHV9ctUKtcbLnTDA==","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":"2026-05-24T23:39:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyCLIKuxHsXjqzsLgFwO4nfR8QUltrDyT0Un2ZrMt7GMTmqrtSeZ7b95mLezZ3uwyQEhThkkiv7lcKJSUQOcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.349551Z"},"content_sha256":"a3ed6f132ed564f9f20605e4477ec963ab0a2748cebc87a897a5a40cba9aaa76","schema_version":"1.0","event_id":"sha256:a3ed6f132ed564f9f20605e4477ec963ab0a2748cebc87a897a5a40cba9aaa76"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://cdn.openai.com/' returned status 404 (The specified resource does not exist.) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://cdn.openai.com/","final_url":"https://cdn.openai.com/","host_kind":"website","status_code":404,"status_text":"The specified resource does not exist.","verdict_class":"incontrovertible","checked_at_unix":1779665745.01622},"severity":"advisory","ref_index":null,"audited_at":"2026-05-24T23:35:46.142622Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://cdn.openai.com/","finding_type":"dead_url","evidence_hash":"1ef51cd0f9f6dab9052107d178515e0da296f9b60e0d43c6f3d40e79af2d971b","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7213,"payload_sha256":"ea52d4cfa72ff7c7faf728ce0b037f66444a7e70def3ab3c81ea48f123966f9f","signature_b64":"FFthyr4WD7S7LWR/FjuVxV1xS4WNKw382stLZTmO3e3wpmYMijVhLdP8yc5JmYPzwwqG3+1mdg/bYstUBlosBA==","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":"2026-05-24T23:39:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/td2sL0bpvP0wJsjR3c2/RU/6MuvmapXgxOyIGeSkUSux8m7HgWdURsbPe7r6hDcaLv6AY0NkgLJXaX0gYTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.349920Z"},"content_sha256":"f647eae439ae333e827c81e2438e1ab4bb74713234c4e3ec2138c7047bb203a7","schema_version":"1.0","event_id":"sha256:f647eae439ae333e827c81e2438e1ab4bb74713234c4e3ec2138c7047bb203a7"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://kellerjordan' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://kellerjordan","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779665744.5824952},"severity":"advisory","ref_index":null,"audited_at":"2026-05-24T23:35:46.142622Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://kellerjordan","finding_type":"dead_url","evidence_hash":"42fb60043e5353b18ba459e0928ea89a90b1a7c7236bacbfd26756fb5eda4f90","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7212,"payload_sha256":"501f3ea59f46700bede1874c8d8f75fc61eeb37f06b28049ffbf6805f030eef3","signature_b64":"QIpprbpJrABEo7ykNTAlLJmqibYtJUI6Gl+lMju3X3bE2lvr3bDV3XnIP8n4psY2TZUr2xgqe4AbqBTL9TziBQ==","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":"2026-05-24T23:39:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KVZSDb+9NUTodSmNi54sWlM4HnIUEK/n170TCqJUu4GB7PiRRoFf3RwfWcSnjxDB88GYxFKdiXDuiCdiHaq5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.350229Z"},"content_sha256":"b0092a12805a46a5d414fc2a7d34e3e09aa7019dc867604e03d870c56bacb621","schema_version":"1.0","event_id":"sha256:b0092a12805a46a5d414fc2a7d34e3e09aa7019dc867604e03d870c56bacb621"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://kellerjordan' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://kellerjordan","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779622533.1900232},"severity":"advisory","ref_index":null,"audited_at":"2026-05-24T11:35:34.754754Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://kellerjordan","finding_type":"dead_url","evidence_hash":"6ff03b052956040ca3a4081cfb2519cf5152c7b5e1c4fd28892c6c968d25297f","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7052,"payload_sha256":"53446404a9089ab643a965e0f3f0cbbb0f655723958637429bd0c954166c36fa","signature_b64":"Wa2Z3Rg2gA3hLbPWRvJi4rjk0fbmpo2yJ8vzj7qn2HzfFYE8WItwm99aR+gdHIywCgbd2rp7IPi7TFqjNe0FAg==","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":"2026-05-24T11:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3QXCyZD0C0KRfJUoDxXZfLQFrUm/Bc4fohZ4cUlNzpR6r09zXlkfR6xHU8PteNzWq/+4t70cLFI/91uk+/gBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.350533Z"},"content_sha256":"f816099a27cd58cd7d08ce53949e10592dd1e16630096939ae55377bd26b3110","schema_version":"1.0","event_id":"sha256:f816099a27cd58cd7d08ce53949e10592dd1e16630096939ae55377bd26b3110"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://link.aps' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://link.aps","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779622533.946121},"severity":"advisory","ref_index":null,"audited_at":"2026-05-24T11:35:34.754754Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://link.aps","finding_type":"dead_url","evidence_hash":"b68478dcaead5a79eabf37e7c71f8b02809fd8a852c12a1ce9063e6be8be741e","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7051,"payload_sha256":"7d3fbe7790ce5c2b9b71ec4b7a5cdddff4fe10ef7695c827dc65f26f165d7158","signature_b64":"/pEuNukCDw4YblMcVD8LfX+hXbiK1hhbn2LaPKb7iifBhk8+4Na02kuNsKY8MdqD9TTC/UVP3NckE5XDquvMAQ==","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":"2026-05-24T11:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hO9e3yEZavMUDEute/jvK7FVWyImsKoQflyVWx80wnTYfnowxzwYoRNcQ5+uwCI1kTPeT92YxMJRqD3lv2evCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.350969Z"},"content_sha256":"5df4e0b2f298019ac4efba9f7397d1ffec764edff48cbc5619fe8c8879c8f90a","schema_version":"1.0","event_id":"sha256:5df4e0b2f298019ac4efba9f7397d1ffec764edff48cbc5619fe8c8879c8f90a"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://cdn.openai.com/' returned status 404 (The specified resource does not exist.) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://cdn.openai.com/","final_url":"https://cdn.openai.com/","host_kind":"website","status_code":404,"status_text":"The specified resource does not exist.","verdict_class":"incontrovertible","checked_at_unix":1779622533.5718305},"severity":"advisory","ref_index":null,"audited_at":"2026-05-24T11:35:34.754754Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://cdn.openai.com/","finding_type":"dead_url","evidence_hash":"96cd1b8d96ffa228ccd8ae99ce905c13a8111c8c132f0d6b4a1c4c57d007043e","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":7050,"payload_sha256":"b9088094dfe03b5a975e5db7384bd1df49f89d93ff1072cc1a95d03303aee387","signature_b64":"ChqWG5dtV3eiSrrAea6Sp1RF6vVCfRCP2Qd5vevOmYuqQN6tLTa0FyiE1sPZ6SXBcxaE37yPE5sisd+WyrReAg==","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":"2026-05-24T11:38:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xIRS/d3yTqvPM3bOK9PwMjLIygK/ZsHyoo70LxiiCJRfW8o0ZVS8xwBo/z07QxhHsL06wTpP2fttOkJBRxiVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.351446Z"},"content_sha256":"ef407c06f3c94c4719a56ef5c716408ef3034cf175734de3bddab7939d78e496","schema_version":"1.0","event_id":"sha256:ef407c06f3c94c4719a56ef5c716408ef3034cf175734de3bddab7939d78e496"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://link.aps' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://link.aps","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779579365.0024135},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T23:36:05.687024Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://link.aps","finding_type":"dead_url","evidence_hash":"5536daf81512d2ec950d0af4154df0cdee0f46c28415d9b855f64766dd8bf4ff","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6886,"payload_sha256":"dbdc7deec533a70ed782480d3c4e79747af1e9da087ecd7654b5dd19baa4c5c6","signature_b64":"lZx1K777swFdzPOftwETneIAZcRue7rpMfM0Vj2yqcZj/3W7upCWEAHb7UJ4cC+MlqkchVCg7FKFU/vn7ODNAw==","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":"2026-05-23T23:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4KNFqJ3nCrnVtMM4vrDVmSqRYZsd5+kYnqBm3U6K7poV/VT6Uj02V3HaIff72N4GZU3kRHCgYK6JN8Z9J+s2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.351742Z"},"content_sha256":"69578583016518db8efe1e7f55725183cde27a0da814ba1bc2a6ebbbcceb6fb6","schema_version":"1.0","event_id":"sha256:69578583016518db8efe1e7f55725183cde27a0da814ba1bc2a6ebbbcceb6fb6"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://cdn.openai.com/' returned status 404 (The specified resource does not exist.) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://cdn.openai.com/","final_url":"https://cdn.openai.com/","host_kind":"website","status_code":404,"status_text":"The specified resource does not exist.","verdict_class":"incontrovertible","checked_at_unix":1779579364.626039},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T23:36:05.687024Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://cdn.openai.com/","finding_type":"dead_url","evidence_hash":"1c788f7dfc10385f4fab50d0f99222703341ba1644438588915097694a010245","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6885,"payload_sha256":"c54cd89c65508d5ee5a8d8a6913bf1eac51def4b4ac2e6a06e667f3180a5a570","signature_b64":"oKOhZcdf8t//zaY5+PW6ocamByDxC7iF7N+GR19C8g9pV6zXrssb4RxVdvaCQVoK/c2HgUvniZthT0yIjsrcDQ==","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":"2026-05-23T23:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2w1RajJ42QcZYmc6Hdt3ncltaqNJj2RO9mfGA3BZWNvDilHpj4n4WclHw+qngJINhT8YNKYsyRVpAAdTtFICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.352097Z"},"content_sha256":"8ba918ab228cf410fef8df5f7a3ce36b05d6ae97ec22745e0fef00e1b68d8a67","schema_version":"1.0","event_id":"sha256:8ba918ab228cf410fef8df5f7a3ce36b05d6ae97ec22745e0fef00e1b68d8a67"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://kellerjordan' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://kellerjordan","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779579364.2221897},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T23:36:05.687024Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://kellerjordan","finding_type":"dead_url","evidence_hash":"19ee8539c132ebccbf81a5dbb439c99ce518c6f7ca4496bda8cc11a67b12aa21","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6884,"payload_sha256":"05d2e6def48d852f17a3466e4bc2dff315fc5f51f6393e627f2a113db534e714","signature_b64":"EfbCWzJWAOikOJ8rc331QikGiWbqOcwePBpwa0FT/dn9th7HuGyrfpcW+DdExf8VfOs/kQC9a97/IAuZxXOCAw==","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":"2026-05-23T23:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHH+xpjSyq+v+rDVLxSA/e4d3rrDz4jz7KkX1Iwv8VTdFoi5tWbcNXAFgrG9V1r+sc1YOQxGObLzubYxMNf2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.352577Z"},"content_sha256":"5c49b39468ec33f07b9ed3ef99c5445f00e1ae2827e64f547ddbbeb627bd4994","schema_version":"1.0","event_id":"sha256:5c49b39468ec33f07b9ed3ef99c5445f00e1ae2827e64f547ddbbeb627bd4994"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://link.aps' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://link.aps","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779536175.909147},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T11:36:16.504924Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://link.aps","finding_type":"dead_url","evidence_hash":"7ccb7704b449c1e51de9eb0967d851d75fbab00da44140c35bd7514f35a2d26f","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6721,"payload_sha256":"598a443a8301133b35c7e3bb25e276460f1b0f79b75fbb1940f05f18c45a0a2d","signature_b64":"05ziHGknEAG3DPVh2WAVMOoBjmsLNlFox+1BTlkUlaRyNtASjsirR0MN0uIUOgiwrkEUF2A7/ENL/udLU0rHBQ==","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":"2026-05-23T11:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WinGLOTd0kFfK75mdOAp+xtnVYo6EksVw+ask2rNpIQ24n0Bp/zsG7sw7jQh13H3sPegTRW7MRgHoz59EBvCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.353058Z"},"content_sha256":"d21fd34b71d7fc3c0622bb05e68c55660d142f03f7ef8cb6b3a9b0f187eb4af2","schema_version":"1.0","event_id":"sha256:d21fd34b71d7fc3c0622bb05e68c55660d142f03f7ef8cb6b3a9b0f187eb4af2"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://cdn.openai.com/' returned status 404 (The specified resource does not exist.) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://cdn.openai.com/","final_url":"https://cdn.openai.com/","host_kind":"website","status_code":404,"status_text":"The specified resource does not exist.","verdict_class":"incontrovertible","checked_at_unix":1779536175.5545335},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T11:36:16.504924Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://cdn.openai.com/","finding_type":"dead_url","evidence_hash":"29c2bef0742d9bc29635005f858a4f77a22735ddc2706a83c16aeb016f6392f5","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6720,"payload_sha256":"1cfff2f7bfd73d696acfeae250688a18ac5e456335ee5edf0c63cf36adf8ea11","signature_b64":"dVcmggY+kdBROwVaV9Z03Swlbe5QG48+N7J+AvoA/95boUmjt5pQCVJxZAbkF4wpXl8OGL71Vpy3WQPf848SDA==","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":"2026-05-23T11:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcHqDyV6ycLW4Ka5KeMUNFYg61dDHpcCG2r6VguAiJWFrqFtNfxYEsvGPuacTu7aQbsMNX33gDVPFI9wXJ88BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.353379Z"},"content_sha256":"3cc3dfccf824b364e07c6f8e2cddb8a65f45a94494af479fddf3c25728fc2ac4","schema_version":"1.0","event_id":"sha256:3cc3dfccf824b364e07c6f8e2cddb8a65f45a94494af479fddf3c25728fc2ac4"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://kellerjordan' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://kellerjordan","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779536175.0840364},"severity":"advisory","ref_index":null,"audited_at":"2026-05-23T11:36:16.504924Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://kellerjordan","finding_type":"dead_url","evidence_hash":"6cf334390af4360f67a6133136f4186d9386c7e0b2d5ec280aec158a8d6e4aeb","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6719,"payload_sha256":"2a5869d7b4a0b2b764f6499f47e2f1c4bbb297e377eb98d0eb9341064cf16ba8","signature_b64":"shuTA098sgbfuqTF5+tqHcOeaAKeSGUP+5MyvhKzB6i4oCL8iv+SVEmzAWfVPNSpZXvMR71TvrPcpb4KUkqsBg==","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":"2026-05-23T11:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b92N7pYfMMe8k5gmYCeJNE1Rk9bPAdyru01qKa0DukqEeoWE2Dt/2f0z0oIaAsZZvGHg13SJuuzzdTltPth+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.353670Z"},"content_sha256":"dd134071f433d7a69a56a901c8c71c69cf5be632e49b14c0d52052eac2dd6349","schema_version":"1.0","event_id":"sha256:dd134071f433d7a69a56a901c8c71c69cf5be632e49b14c0d52052eac2dd6349"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://link.aps' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://link.aps","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779492946.320567},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T23:35:47.062077Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://link.aps","finding_type":"dead_url","evidence_hash":"f161983a5ee9921e2e4fe1c9b8c18aad69312b9203f68dea8a5979fbc7ac0150","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6555,"payload_sha256":"11f927a119813325328cd394b362bbaeb13a8afa25653e6c7a6cb4ffecdcaa92","signature_b64":"neQOsIHHpb/9pNnxP56ys/XRoK1o3wxoK+8MzVXTiZgBBeYcQGG8WM5BLgN2YLPMVGFMI6txjezZLvkeyGQaCg==","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":"2026-05-22T23:36:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6awUEZAvr5piFPSLChM0qFIpc5UYK8nwKkFZ5XNWDiU7BVuZIdTvJmkNGI5X2Zhhkiy/EkJ2LfYrE6i6gB05Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.354185Z"},"content_sha256":"392a7795097febabb0805a75c2a512622bf5530a6fb878c69338570822bb3d44","schema_version":"1.0","event_id":"sha256:392a7795097febabb0805a75c2a512622bf5530a6fb878c69338570822bb3d44"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://cdn.openai.com/' returned status 404 (The specified resource does not exist.) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://cdn.openai.com/","final_url":"https://cdn.openai.com/","host_kind":"website","status_code":404,"status_text":"The specified resource does not exist.","verdict_class":"incontrovertible","checked_at_unix":1779492946.1275663},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T23:35:47.062077Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://cdn.openai.com/","finding_type":"dead_url","evidence_hash":"7967e5c66d4e6ca6a9b41d03246baf6f7238783c048a828880e89d2601d5e839","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6554,"payload_sha256":"21161927377dd621b27803925567977586e8a2f19097772b3a5e5bb82a221ef1","signature_b64":"Jr+wO4Ilkng5DxkAClDgKVZVg+UHSqLdQLSCDnMfDS2f3AJGC2V6JtoXygkgeBTrhn8g2NxFgOYivZ1gt5LBAg==","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":"2026-05-22T23:36:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+vetjKkNwvFbPxvpBTxi/G1tS780J1pZavWaObQptfPqu5qSgTXEbigNSUi6xmICI6es3At88MlWyE3fNc6fCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.354723Z"},"content_sha256":"d067af1811425bff992f97f8119e6a123a5794c7323e493d7b6b7807254906f6","schema_version":"1.0","event_id":"sha256:d067af1811425bff992f97f8119e6a123a5794c7323e493d7b6b7807254906f6"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://kellerjordan' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://kellerjordan","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779492945.689089},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T23:35:47.062077Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://kellerjordan","finding_type":"dead_url","evidence_hash":"eef20501edb9be64805406e2d9ef0feaecc76a7930b2907c445ca266ab2e6f70","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6553,"payload_sha256":"143620d6aa70f5111c4b102a125ef417300effa0bdf1d2e4de2c892e8b34ce93","signature_b64":"Z81QqvWoYf7pmbv+02rMGH1OD31mecAVxKAQ7YajhRjMbGt6u8PVl8PDMBUXANpA0ILKPS1jcGr1I8V8UPpuBA==","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":"2026-05-22T23:36:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"APLh2Xq/r41r0AV1em2a6+3CA7KA26zOoMYMOXJYA9QgyN1H3n7SkWOOKjRDC8IuRLQX50MoP5Bkag8d9/+BAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.355250Z"},"content_sha256":"9ecdd419f04b9980b200eb413af4351f3021c7759bddb01e6e7adbf06f35e981","schema_version":"1.0","event_id":"sha256:9ecdd419f04b9980b200eb413af4351f3021c7759bddb01e6e7adbf06f35e981"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://link.aps' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://link.aps","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779449733.2706792},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T11:35:34.066700Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://link.aps","finding_type":"dead_url","evidence_hash":"7fdd92078d6631f51f1282d91775b9fe05ea8318934b75a6cdedc6ef38786663","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6381,"payload_sha256":"ad11031a3cb2154d0856453fd73b241302d6fed89c667186dabeae1d3a31ded2","signature_b64":"6ypqmlo+jdDTMifhtIsqT5/uRcm6OF43Yl6ugBr78WO+KVL9UfLgeCRsqijMTsiW4TduxQWeco1muig+A8wCAw==","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":"2026-05-22T11:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m09tO+Qfd8i/vNuUKF1ESdeo7p6sEk5ee5JzA26B2gRqEDzgR5lm0rkQR+cgGIDj/i0GnHE12ZJq5HugHm1CCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.355761Z"},"content_sha256":"99cf121c9faff334d406a1bf442a9b11398c4ae2eb4a04562f5965e5daacd8bf","schema_version":"1.0","event_id":"sha256:99cf121c9faff334d406a1bf442a9b11398c4ae2eb4a04562f5965e5daacd8bf"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://cdn.openai.com/' returned status 404 (The specified resource does not exist.) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://cdn.openai.com/","final_url":"https://cdn.openai.com/","host_kind":"website","status_code":404,"status_text":"The specified resource does not exist.","verdict_class":"incontrovertible","checked_at_unix":1779449732.9564137},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T11:35:34.066700Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://cdn.openai.com/","finding_type":"dead_url","evidence_hash":"34994f158462dc287a37cd3bd9be936f16d5a1bee4b3a329d3ca1403a8c8e89e","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6380,"payload_sha256":"b927a19b814b38cae4274df9050c4a8dac822b2d02d36daefa4a0ad7db14cc8d","signature_b64":"mmp1qRL8dGoa9P9hF9MvM9xLNE5m3Hk4/GBE7z+ect+IlOocwPSh4XnQ2a0MOgdNmwa0ASUVn/skNYpyE3qnDA==","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":"2026-05-22T11:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9bBNhhqzw3gQFTJ7UHTQm0XHfIARuVHdCF7j/GSrUnnfhfa28jNH3QcgBltqCCIMfJ4xSmgcbvmx5VW/RBCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.356091Z"},"content_sha256":"e0ae48472c5ecd3851d9540e849009d7dc8dd346d00327ad747573c92143994c","schema_version":"1.0","event_id":"sha256:e0ae48472c5ecd3851d9540e849009d7dc8dd346d00327ad747573c92143994c"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","target":"integrity","payload":{"note":"URL 'https://kellerjordan' returned status transport error (transport error: [Errno -3] Temporary failure in name resolution) at last check.","snippet":null,"arxiv_id":"2605.22644","detector":"external_links","evidence":{"url":"https://kellerjordan","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -3] Temporary failure in name resolution","verdict_class":"incontrovertible","checked_at_unix":1779449732.5095532},"severity":"advisory","ref_index":null,"audited_at":"2026-05-22T11:35:34.066700Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"https://kellerjordan","finding_type":"dead_url","evidence_hash":"dc6a303261707e5a2192e989dbed06ad96a7057a747213922441770d875d57c8","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6379,"payload_sha256":"dbc18c1d4e5053f1605cc1ad7452644c1e50c63fe7cb9cef8e29706b6009129b","signature_b64":"eOmVIiPmENVx03k5LEpk0XAU0Kvo0mUItOZBUVfFB2OmB2tTtYbEgNzUxW/w61anmw1kbdOM+py6s68AJgS3BQ==","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":"2026-05-22T11:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5iQnGUjOqn3CFAC+CW+a0A34enQi28ZN51HBzaIIbWSmsApTDgh3Os/Dqs3ZFD7uC1z6lbMk4QaYe/KqCAXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:22:44.356377Z"},"content_sha256":"ee9a93891f92257553472a6d27f6f7a1e5a9617b3ad69f120f4e8cf248b0c146","schema_version":"1.0","event_id":"sha256:ee9a93891f92257553472a6d27f6f7a1e5a9617b3ad69f120f4e8cf248b0c146"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P64LSTQD5GRW6FSBZBI6SNLXMI/bundle.json","state_url":"https://pith.science/pith/P64LSTQD5GRW6FSBZBI6SNLXMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P64LSTQD5GRW6FSBZBI6SNLXMI/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":"2026-05-25T03:22:44Z","links":{"resolver":"https://pith.science/pith/P64LSTQD5GRW6FSBZBI6SNLXMI","bundle":"https://pith.science/pith/P64LSTQD5GRW6FSBZBI6SNLXMI/bundle.json","state":"https://pith.science/pith/P64LSTQD5GRW6FSBZBI6SNLXMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P64LSTQD5GRW6FSBZBI6SNLXMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","merge_version":"pith-open-graph-merge-v1","event_count":20,"valid_event_count":20,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86358fed8f0b2c5b763c46a67567acd2db7861d37ea499e960bd86a0f3814076","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","title_canon_sha256":"5aa39333e0097b93ef5577f5d61f8beb309f0718bb37441e8ea24c6114e3911a"},"schema_version":"1.0","source":{"id":"2605.22644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22644","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22644v1","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22644","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"P64LSTQD5GRW","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"P64LSTQD5GRW6FSB","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"P64LSTQD","created_at":"2026-05-22T02:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:48d38dca88793d03e3d0ce638b9111a0cb819463557ad30b6181e17b7033eea9","target":"graph","created_at":"2026-05-22T02:04:47Z","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/2605.22644/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Stochastic Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion. However, this approximation relies on a continuous-time limit and a sqrt(eta) noise scaling that does not match the discrete SGD update at finite learning rate. In this work, we propose an alternative formulation of SGD as deterministic dynamics in a fluctuating loss landscape induced by minibatch sampling. Starting directly from the discrete update, we derive a master equation for the parameter distribution and obtain a discrete Fokker--Planck equation that diffe","authors_text":"Aleksandr Beznosikov, Aleksandr Kovalenko, Aleksandr Shestakov, Andrew Semenov, Andrey Leonidov, Andrey Veprikov, Anna Radovskaya, Egor Lopatin, Igor Ignashin, Stanislav Potapov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","title":"Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22644","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:fe796f1e00f070f18bd74b3f40f98517928581d251121e93caaaa4200703be30","target":"record","created_at":"2026-05-22T02:04:47Z","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":"86358fed8f0b2c5b763c46a67567acd2db7861d37ea499e960bd86a0f3814076","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","title_canon_sha256":"5aa39333e0097b93ef5577f5d61f8beb309f0718bb37441e8ea24c6114e3911a"},"schema_version":"1.0","source":{"id":"2605.22644","kind":"arxiv","version":1}},"canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","first_computed_at":"2026-05-22T02:04:47.754035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:47.754035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVao27D8qov53dxfL6iLwJgcdMkl4pjsV5Q+JvK1DiCN2kZF4ymssvUVtiPYg+yypP79LafNmMwbjCpJdXVZDw==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:47.754876Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22644","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:392a7795097febabb0805a75c2a512622bf5530a6fb878c69338570822bb3d44","sha256:3cc3dfccf824b364e07c6f8e2cddb8a65f45a94494af479fddf3c25728fc2ac4","sha256:5c49b39468ec33f07b9ed3ef99c5445f00e1ae2827e64f547ddbbeb627bd4994","sha256:5df4e0b2f298019ac4efba9f7397d1ffec764edff48cbc5619fe8c8879c8f90a","sha256:69578583016518db8efe1e7f55725183cde27a0da814ba1bc2a6ebbbcceb6fb6","sha256:8ba918ab228cf410fef8df5f7a3ce36b05d6ae97ec22745e0fef00e1b68d8a67","sha256:99cf121c9faff334d406a1bf442a9b11398c4ae2eb4a04562f5965e5daacd8bf","sha256:9ecdd419f04b9980b200eb413af4351f3021c7759bddb01e6e7adbf06f35e981","sha256:a3ed6f132ed564f9f20605e4477ec963ab0a2748cebc87a897a5a40cba9aaa76","sha256:b0092a12805a46a5d414fc2a7d34e3e09aa7019dc867604e03d870c56bacb621","sha256:d067af1811425bff992f97f8119e6a123a5794c7323e493d7b6b7807254906f6","sha256:d21fd34b71d7fc3c0622bb05e68c55660d142f03f7ef8cb6b3a9b0f187eb4af2","sha256:dd134071f433d7a69a56a901c8c71c69cf5be632e49b14c0d52052eac2dd6349","sha256:e0ae48472c5ecd3851d9540e849009d7dc8dd346d00327ad747573c92143994c","sha256:ee9a93891f92257553472a6d27f6f7a1e5a9617b3ad69f120f4e8cf248b0c146","sha256:ef407c06f3c94c4719a56ef5c716408ef3034cf175734de3bddab7939d78e496","sha256:f647eae439ae333e827c81e2438e1ab4bb74713234c4e3ec2138c7047bb203a7","sha256:f816099a27cd58cd7d08ce53949e10592dd1e16630096939ae55377bd26b3110"]}],"invalid_events":[],"applied_event_ids":["sha256:fe796f1e00f070f18bd74b3f40f98517928581d251121e93caaaa4200703be30","sha256:48d38dca88793d03e3d0ce638b9111a0cb819463557ad30b6181e17b7033eea9"],"state_sha256":"87f684956d8f6c892b69059707deeafac7183d8c7f7a0fb8fe4dde141e771e8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2f3R9NrRN9iNAbdyT1/03g8pME9Cj9o4JwuGzuIwjnSldGKbwP3MCRJFtxlSM1y8gK5sMgVJCN6vd6HnbV2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T03:22:44.363160Z","bundle_sha256":"eeb067c4c34eaf17975006577ed93feba209a4b37da9dc131655795263946b99"}}