{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DNDHAZCM776C5EBL6JOVRWJNLJ","short_pith_number":"pith:DNDHAZCM","canonical_record":{"source":{"id":"2111.08162","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-16T00:51:22Z","cross_cats_sorted":[],"title_canon_sha256":"3f8646be75aeda0a5ef3fcd73b536307b83041f8d5e8240db9a94ce8bd40ce1c","abstract_canon_sha256":"99eca7cb012b2e9f1df7da679e870a0254896e0c903a2f19fc0458cfbc6b4188"},"schema_version":"1.0"},"canonical_sha256":"1b4670644cfffc2e902bf25d58d92d5a6fe25a547aa1c353d538837f1ec45a10","source":{"kind":"arxiv","id":"2111.08162","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.08162","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"2111.08162v4","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.08162","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"DNDHAZCM776C","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"pith_short_16","alias_value":"DNDHAZCM776C5EBL","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"pith_short_8","alias_value":"DNDHAZCM","created_at":"2026-07-05T04:55:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DNDHAZCM776C5EBL6JOVRWJNLJ","target":"record","payload":{"canonical_record":{"source":{"id":"2111.08162","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-16T00:51:22Z","cross_cats_sorted":[],"title_canon_sha256":"3f8646be75aeda0a5ef3fcd73b536307b83041f8d5e8240db9a94ce8bd40ce1c","abstract_canon_sha256":"99eca7cb012b2e9f1df7da679e870a0254896e0c903a2f19fc0458cfbc6b4188"},"schema_version":"1.0"},"canonical_sha256":"1b4670644cfffc2e902bf25d58d92d5a6fe25a547aa1c353d538837f1ec45a10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:55:50.188131Z","signature_b64":"BIJJhmtQNeriN2lHztEKGHA6ovL6FyWSAii4qSv4yqn7Ugxs0FweKZXHSLswdcoqsBnvLlhOiBPMPc4zwcYDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b4670644cfffc2e902bf25d58d92d5a6fe25a547aa1c353d538837f1ec45a10","last_reissued_at":"2026-07-05T04:55:50.187689Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:55:50.187689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.08162","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:55:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ATsZoeg5js7HZHnfeLdgfy0yd5V8URlt+4WxqzolM81hgeMBrzH7PTuUm+lr96QQeLp0Jam7PBzR7CbxvIFkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:15:57.211856Z"},"content_sha256":"7235b30c4bf349c61b9b622647469d8b0852928cda5a1ffd73c260579e039a0b","schema_version":"1.0","event_id":"sha256:7235b30c4bf349c61b9b622647469d8b0852928cda5a1ffd73c260579e039a0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DNDHAZCM776C5EBL6JOVRWJNLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Conjecture Regarding the Adam Optimizer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Douglas Tweed, Mohamed Akrout","submitted_at":"2021-11-16T00:51:22Z","abstract_excerpt":"Why does the Adam optimizer work so well in deep-learning applications? Adam's originators, Kingma and Ba, presented a mathematical argument that was meant to help explain its success, but Bock and colleagues have since reported that a key piece is missing from that argument $-$ an unproven lemma which we will call Bock's conjecture. Here we show that this conjecture is false, but we prove a modified version of it $-$ a generalization of a result of Reddi and colleagues $-$ which can take its place in analyses of Adam."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.08162","kind":"arxiv","version":4},"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/2111.08162/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":"2026-07-05T04:55:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sgTw3Oy4ph0U2GfmfDQEjU7FMejn0+JEc1P+ed0AyIFr+SOWn889f6riN5UO16eZLSWj3Uw/dqfh8h/RWqtmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:15:57.225779Z"},"content_sha256":"22b1a80eb871cb9bb246a505e83b6be01c2125f1bc14dafcbc5a4606003f1b3f","schema_version":"1.0","event_id":"sha256:22b1a80eb871cb9bb246a505e83b6be01c2125f1bc14dafcbc5a4606003f1b3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNDHAZCM776C5EBL6JOVRWJNLJ/bundle.json","state_url":"https://pith.science/pith/DNDHAZCM776C5EBL6JOVRWJNLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNDHAZCM776C5EBL6JOVRWJNLJ/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":"2026-08-05T06:15:57Z","links":{"resolver":"https://pith.science/pith/DNDHAZCM776C5EBL6JOVRWJNLJ","bundle":"https://pith.science/pith/DNDHAZCM776C5EBL6JOVRWJNLJ/bundle.json","state":"https://pith.science/pith/DNDHAZCM776C5EBL6JOVRWJNLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNDHAZCM776C5EBL6JOVRWJNLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DNDHAZCM776C5EBL6JOVRWJNLJ","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":"99eca7cb012b2e9f1df7da679e870a0254896e0c903a2f19fc0458cfbc6b4188","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-16T00:51:22Z","title_canon_sha256":"3f8646be75aeda0a5ef3fcd73b536307b83041f8d5e8240db9a94ce8bd40ce1c"},"schema_version":"1.0","source":{"id":"2111.08162","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.08162","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"2111.08162v4","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.08162","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"DNDHAZCM776C","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"pith_short_16","alias_value":"DNDHAZCM776C5EBL","created_at":"2026-07-05T04:55:50Z"},{"alias_kind":"pith_short_8","alias_value":"DNDHAZCM","created_at":"2026-07-05T04:55:50Z"}],"graph_snapshots":[{"event_id":"sha256:22b1a80eb871cb9bb246a505e83b6be01c2125f1bc14dafcbc5a4606003f1b3f","target":"graph","created_at":"2026-07-05T04:55:50Z","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/2111.08162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Why does the Adam optimizer work so well in deep-learning applications? Adam's originators, Kingma and Ba, presented a mathematical argument that was meant to help explain its success, but Bock and colleagues have since reported that a key piece is missing from that argument $-$ an unproven lemma which we will call Bock's conjecture. Here we show that this conjecture is false, but we prove a modified version of it $-$ a generalization of a result of Reddi and colleagues $-$ which can take its place in analyses of Adam.","authors_text":"Douglas Tweed, Mohamed Akrout","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-16T00:51:22Z","title":"On a Conjecture Regarding the Adam Optimizer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.08162","kind":"arxiv","version":4},"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":"sha256:7235b30c4bf349c61b9b622647469d8b0852928cda5a1ffd73c260579e039a0b","target":"record","created_at":"2026-07-05T04:55:50Z","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":"99eca7cb012b2e9f1df7da679e870a0254896e0c903a2f19fc0458cfbc6b4188","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-11-16T00:51:22Z","title_canon_sha256":"3f8646be75aeda0a5ef3fcd73b536307b83041f8d5e8240db9a94ce8bd40ce1c"},"schema_version":"1.0","source":{"id":"2111.08162","kind":"arxiv","version":4}},"canonical_sha256":"1b4670644cfffc2e902bf25d58d92d5a6fe25a547aa1c353d538837f1ec45a10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b4670644cfffc2e902bf25d58d92d5a6fe25a547aa1c353d538837f1ec45a10","first_computed_at":"2026-07-05T04:55:50.187689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:55:50.187689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BIJJhmtQNeriN2lHztEKGHA6ovL6FyWSAii4qSv4yqn7Ugxs0FweKZXHSLswdcoqsBnvLlhOiBPMPc4zwcYDBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:55:50.188131Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.08162","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7235b30c4bf349c61b9b622647469d8b0852928cda5a1ffd73c260579e039a0b","sha256:22b1a80eb871cb9bb246a505e83b6be01c2125f1bc14dafcbc5a4606003f1b3f"],"state_sha256":"5c217b82826007468abafa8a0f684bb34e6ed588d7b34616e71674d91f9fdc43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yDVfl/jR115dw91NeTGkxj0LUwN9IbLdteYsyhXtAUxTSB3nP3js9KP9qnRhPh5Dp3UxUOXQesSXZ7nXtQIqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T06:15:57.291760Z","bundle_sha256":"590efbb8c4cfc1db6ceca76901936d476954a1169d1310e2424a936e5921bbd5"}}