{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VYISZY2ZAU65DMUP27KXWAIOM7","short_pith_number":"pith:VYISZY2Z","canonical_record":{"source":{"id":"2606.24543","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-23T13:07:39Z","cross_cats_sorted":[],"title_canon_sha256":"08516e07a2280d861edcedd6673b43ea6f882a70201410bea627f1e30f715974","abstract_canon_sha256":"f1487e96cf329452dcf12d7090b78e479c78575d2da36c367dda9db839a45d46"},"schema_version":"1.0"},"canonical_sha256":"ae112ce359053dd1b28fd7d57b010e67ce6074465f360b2b3f4acffdf05b61cf","source":{"kind":"arxiv","id":"2606.24543","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24543","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24543v1","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24543","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"VYISZY2ZAU65","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_16","alias_value":"VYISZY2ZAU65DMUP","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_8","alias_value":"VYISZY2Z","created_at":"2026-06-24T01:15:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VYISZY2ZAU65DMUP27KXWAIOM7","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24543","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-23T13:07:39Z","cross_cats_sorted":[],"title_canon_sha256":"08516e07a2280d861edcedd6673b43ea6f882a70201410bea627f1e30f715974","abstract_canon_sha256":"f1487e96cf329452dcf12d7090b78e479c78575d2da36c367dda9db839a45d46"},"schema_version":"1.0"},"canonical_sha256":"ae112ce359053dd1b28fd7d57b010e67ce6074465f360b2b3f4acffdf05b61cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:33.438070Z","signature_b64":"LhlqTY1pVgmP1RfWE18ekmU6GREZJfgz8FdMRd2R1sNwrTIu304bUMZH0WXT5kNbY9QFxXdH2xgSG/w/RAdXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae112ce359053dd1b28fd7d57b010e67ce6074465f360b2b3f4acffdf05b61cf","last_reissued_at":"2026-06-24T01:15:33.437724Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:33.437724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24543","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":"2026-06-24T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5yxxUI0Ch6WV6b5HspYn7psS7hZF7Rjf78p7mcinAY5wMq33qkgLVZDu3EB9lgpzqZ0z9jQjJyf+9BqsoWGJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:47:16.704528Z"},"content_sha256":"a000a0fa5a81d30a21f517b9dcb1200e48186edf49ef6c27c48c1330e60d1cd4","schema_version":"1.0","event_id":"sha256:a000a0fa5a81d30a21f517b9dcb1200e48186edf49ef6c27c48c1330e60d1cd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VYISZY2ZAU65DMUP27KXWAIOM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reasoning as Attractor Dynamics: Latent Memory Retrieval via Gibbs-Weighted Energy Minimization","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kanishk Awadhiya","submitted_at":"2026-06-23T13:07:39Z","abstract_excerpt":"Large Language Models (LLMs) are traditionally viewed as autoregressive generators. However, from the perspective of collective computation, they function as high-dimensional Dense Associative Memories that store complex reasoning patterns as latent attractors. In this work, we investigate the energy landscape of mathematical reasoning. We posit that correct reasoning chains correspond to deep, wide attractor basins (\"flat minima\") in the model's output distribution, whereas hallucinations manifest as sharp, unstable local minima. To exploit this geometry, we introduce a retrieval mechanism ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24543","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/2606.24543/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":"2026-06-24T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ti6TuyT94kE2FoRm0x6fdlrsQCfloJg5o6KtKZTWAPFtC8FI+yXMb4coTk2oOmZpWh9pg2rgGtbOJ0tPFRa4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:47:16.704894Z"},"content_sha256":"1f0ba5346c657c45d06bd1b066eaad0da9ef02c50eb488734a20427945450a42","schema_version":"1.0","event_id":"sha256:1f0ba5346c657c45d06bd1b066eaad0da9ef02c50eb488734a20427945450a42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYISZY2ZAU65DMUP27KXWAIOM7/bundle.json","state_url":"https://pith.science/pith/VYISZY2ZAU65DMUP27KXWAIOM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYISZY2ZAU65DMUP27KXWAIOM7/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":"2026-07-04T22:47:16Z","links":{"resolver":"https://pith.science/pith/VYISZY2ZAU65DMUP27KXWAIOM7","bundle":"https://pith.science/pith/VYISZY2ZAU65DMUP27KXWAIOM7/bundle.json","state":"https://pith.science/pith/VYISZY2ZAU65DMUP27KXWAIOM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYISZY2ZAU65DMUP27KXWAIOM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VYISZY2ZAU65DMUP27KXWAIOM7","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":"f1487e96cf329452dcf12d7090b78e479c78575d2da36c367dda9db839a45d46","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-23T13:07:39Z","title_canon_sha256":"08516e07a2280d861edcedd6673b43ea6f882a70201410bea627f1e30f715974"},"schema_version":"1.0","source":{"id":"2606.24543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24543","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24543v1","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24543","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"VYISZY2ZAU65","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_16","alias_value":"VYISZY2ZAU65DMUP","created_at":"2026-06-24T01:15:33Z"},{"alias_kind":"pith_short_8","alias_value":"VYISZY2Z","created_at":"2026-06-24T01:15:33Z"}],"graph_snapshots":[{"event_id":"sha256:1f0ba5346c657c45d06bd1b066eaad0da9ef02c50eb488734a20427945450a42","target":"graph","created_at":"2026-06-24T01:15:33Z","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/2606.24543/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large Language Models (LLMs) are traditionally viewed as autoregressive generators. However, from the perspective of collective computation, they function as high-dimensional Dense Associative Memories that store complex reasoning patterns as latent attractors. In this work, we investigate the energy landscape of mathematical reasoning. We posit that correct reasoning chains correspond to deep, wide attractor basins (\"flat minima\") in the model's output distribution, whereas hallucinations manifest as sharp, unstable local minima. To exploit this geometry, we introduce a retrieval mechanism ba","authors_text":"Kanishk Awadhiya","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-23T13:07:39Z","title":"Reasoning as Attractor Dynamics: Latent Memory Retrieval via Gibbs-Weighted Energy Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24543","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:a000a0fa5a81d30a21f517b9dcb1200e48186edf49ef6c27c48c1330e60d1cd4","target":"record","created_at":"2026-06-24T01:15:33Z","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":"f1487e96cf329452dcf12d7090b78e479c78575d2da36c367dda9db839a45d46","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-23T13:07:39Z","title_canon_sha256":"08516e07a2280d861edcedd6673b43ea6f882a70201410bea627f1e30f715974"},"schema_version":"1.0","source":{"id":"2606.24543","kind":"arxiv","version":1}},"canonical_sha256":"ae112ce359053dd1b28fd7d57b010e67ce6074465f360b2b3f4acffdf05b61cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae112ce359053dd1b28fd7d57b010e67ce6074465f360b2b3f4acffdf05b61cf","first_computed_at":"2026-06-24T01:15:33.437724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:33.437724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LhlqTY1pVgmP1RfWE18ekmU6GREZJfgz8FdMRd2R1sNwrTIu304bUMZH0WXT5kNbY9QFxXdH2xgSG/w/RAdXBg==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:33.438070Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a000a0fa5a81d30a21f517b9dcb1200e48186edf49ef6c27c48c1330e60d1cd4","sha256:1f0ba5346c657c45d06bd1b066eaad0da9ef02c50eb488734a20427945450a42"],"state_sha256":"a6e2df0308ac98c15d1e02cf8a7219028b81192d7327bcea07a3ad014f11fcce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KkSYRM78l/bUYjJpMyoXfZm0ydoqnXzrP4IzhtBho++NkeNFcZe6diVBBCNuFupuuTWfAuP6M/8CN0JmXp77Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T22:47:16.706917Z","bundle_sha256":"6d58e831fd6536e7a495a673a1166a1f15eeb45c64b27abff25be122b900d779"}}