{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UUVNL2ICMCBMNAGPG6EGPOAJMW","short_pith_number":"pith:UUVNL2IC","canonical_record":{"source":{"id":"2410.11781","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-15T17:00:15Z","cross_cats_sorted":[],"title_canon_sha256":"3e32c89b51524751a982116fe443eefdba6d3fbf35ec44278613608cb6a211cb","abstract_canon_sha256":"32876d2845236133a6904aa7f1535426066a786f6e8e416209af9fafcfdd172a"},"schema_version":"1.0"},"canonical_sha256":"a52ad5e9026082c680cf378867b80965b443e24085d7de04751242a606593eb0","source":{"kind":"arxiv","id":"2410.11781","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.11781","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2410.11781v2","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.11781","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"UUVNL2ICMCBM","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"UUVNL2ICMCBMNAGP","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"UUVNL2IC","created_at":"2026-07-05T10:08:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UUVNL2ICMCBMNAGPG6EGPOAJMW","target":"record","payload":{"canonical_record":{"source":{"id":"2410.11781","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-15T17:00:15Z","cross_cats_sorted":[],"title_canon_sha256":"3e32c89b51524751a982116fe443eefdba6d3fbf35ec44278613608cb6a211cb","abstract_canon_sha256":"32876d2845236133a6904aa7f1535426066a786f6e8e416209af9fafcfdd172a"},"schema_version":"1.0"},"canonical_sha256":"a52ad5e9026082c680cf378867b80965b443e24085d7de04751242a606593eb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:22.797981Z","signature_b64":"vMyMaw7Ozm3qrVoteWCHgHIzZQzAUg4p+reFDlHXtxro7+LecRd01w9v4W6BKYnbyZm0jOYXdBCi1Ya7kBhKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a52ad5e9026082c680cf378867b80965b443e24085d7de04751242a606593eb0","last_reissued_at":"2026-07-05T10:08:22.797558Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:22.797558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.11781","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/XFMX3iqlcUCkAFx4qR2mfpNpTSKF1nx6OeHi0LnZ3own+GIQG4pOXOe7MZEcaevq0AyDk90uEEhFAlI0W1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:27:59.656658Z"},"content_sha256":"597fbf9761e8e185639fdbb9980540f7880d447bf1162bfdbfd73b2359278d57","schema_version":"1.0","event_id":"sha256:597fbf9761e8e185639fdbb9980540f7880d447bf1162bfdbfd73b2359278d57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UUVNL2ICMCBMNAGPG6EGPOAJMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Language Models Encode Numbers Using Digit Representations in Base 10","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Amit Arnold Levy, Mor Geva","submitted_at":"2024-10-15T17:00:15Z","abstract_excerpt":"Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether their representations of numbers capture their numeric values. We tackle this question from the observation that LLM errors on numerical tasks are often distributed across the digits of the answer rather than normally around its numeric value. Through a series of probing experiments and causal interventions, we show that LLMs internally represent numbers wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.11781","kind":"arxiv","version":2},"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/2410.11781/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":"2026-07-05T10:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPtYBQBLMCCQ0W50OBNUmpqao1r1ZtM74hIphFrKZBNhEsfkW6rsxCJKP2uPDGShJ1Pa4vBxccIothIwHYyaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:27:59.657575Z"},"content_sha256":"c7fb6dc93d6e8572ee7540db825382a9d11fbc19afd3f5a44471b6878fa24e0a","schema_version":"1.0","event_id":"sha256:c7fb6dc93d6e8572ee7540db825382a9d11fbc19afd3f5a44471b6878fa24e0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW/bundle.json","state_url":"https://pith.science/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW/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":"2026-08-18T18:27:59Z","links":{"resolver":"https://pith.science/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW","bundle":"https://pith.science/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW/bundle.json","state":"https://pith.science/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUVNL2ICMCBMNAGPG6EGPOAJMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UUVNL2ICMCBMNAGPG6EGPOAJMW","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":"32876d2845236133a6904aa7f1535426066a786f6e8e416209af9fafcfdd172a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-15T17:00:15Z","title_canon_sha256":"3e32c89b51524751a982116fe443eefdba6d3fbf35ec44278613608cb6a211cb"},"schema_version":"1.0","source":{"id":"2410.11781","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.11781","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"2410.11781v2","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.11781","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"UUVNL2ICMCBM","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"UUVNL2ICMCBMNAGP","created_at":"2026-07-05T10:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"UUVNL2IC","created_at":"2026-07-05T10:08:22Z"}],"graph_snapshots":[{"event_id":"sha256:c7fb6dc93d6e8572ee7540db825382a9d11fbc19afd3f5a44471b6878fa24e0a","target":"graph","created_at":"2026-07-05T10:08:22Z","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/2410.11781/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether their representations of numbers capture their numeric values. We tackle this question from the observation that LLM errors on numerical tasks are often distributed across the digits of the answer rather than normally around its numeric value. Through a series of probing experiments and causal interventions, we show that LLMs internally represent numbers wi","authors_text":"Amit Arnold Levy, Mor Geva","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-15T17:00:15Z","title":"Language Models Encode Numbers Using Digit Representations in Base 10"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.11781","kind":"arxiv","version":2},"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":"sha256:597fbf9761e8e185639fdbb9980540f7880d447bf1162bfdbfd73b2359278d57","target":"record","created_at":"2026-07-05T10:08:22Z","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":"32876d2845236133a6904aa7f1535426066a786f6e8e416209af9fafcfdd172a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-15T17:00:15Z","title_canon_sha256":"3e32c89b51524751a982116fe443eefdba6d3fbf35ec44278613608cb6a211cb"},"schema_version":"1.0","source":{"id":"2410.11781","kind":"arxiv","version":2}},"canonical_sha256":"a52ad5e9026082c680cf378867b80965b443e24085d7de04751242a606593eb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a52ad5e9026082c680cf378867b80965b443e24085d7de04751242a606593eb0","first_computed_at":"2026-07-05T10:08:22.797558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:08:22.797558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vMyMaw7Ozm3qrVoteWCHgHIzZQzAUg4p+reFDlHXtxro7+LecRd01w9v4W6BKYnbyZm0jOYXdBCi1Ya7kBhKBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:08:22.797981Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.11781","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:597fbf9761e8e185639fdbb9980540f7880d447bf1162bfdbfd73b2359278d57","sha256:c7fb6dc93d6e8572ee7540db825382a9d11fbc19afd3f5a44471b6878fa24e0a"],"state_sha256":"1735453d7e741cda2943792e0f3a0e77ab112763013eff73b57d91a301c5bb3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52sh3EHeURpEbJ20f36jqEFqoWAu/o65ew4tTwB2DWoeDy6+qufbxbnv72jPdFmejzJLWXg2jYFKa9bSBDceCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:27:59.662937Z","bundle_sha256":"d14efe8d3334f5606fd1304b9d3097cffe4b407673ac42c4b6b4ff101909a10f"}}