{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:K6GIN7VUVBEJ2AS3YRZBW36LSE","short_pith_number":"pith:K6GIN7VU","canonical_record":{"source":{"id":"2109.07230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2021-09-15T11:54:28Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"73c8e8902f6cfe79612ef5c3444d0fc7bf3926c00311bc4c4acbcbd07a3ee8ad","abstract_canon_sha256":"380a485dc416612d8136fb926fdb0733941b89cf86fb438188afc2536329e913"},"schema_version":"1.0"},"canonical_sha256":"578c86feb4a8489d025bc4721b6fcb9102cb5f83df741a75529d0b86d6b2805e","source":{"kind":"arxiv","id":"2109.07230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.07230","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"2109.07230v1","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.07230","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"K6GIN7VUVBEJ","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"pith_short_16","alias_value":"K6GIN7VUVBEJ2AS3","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"pith_short_8","alias_value":"K6GIN7VU","created_at":"2026-07-05T03:14:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:K6GIN7VUVBEJ2AS3YRZBW36LSE","target":"record","payload":{"canonical_record":{"source":{"id":"2109.07230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2021-09-15T11:54:28Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"73c8e8902f6cfe79612ef5c3444d0fc7bf3926c00311bc4c4acbcbd07a3ee8ad","abstract_canon_sha256":"380a485dc416612d8136fb926fdb0733941b89cf86fb438188afc2536329e913"},"schema_version":"1.0"},"canonical_sha256":"578c86feb4a8489d025bc4721b6fcb9102cb5f83df741a75529d0b86d6b2805e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:14:40.124014Z","signature_b64":"fMTcJib8snDQBj1uRu6g+hOIadTAt8IZpU80ZC3MUUPCmhP53Eqe6niGzrKb700VzeRtzoUIopqv/juq6qmFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578c86feb4a8489d025bc4721b6fcb9102cb5f83df741a75529d0b86d6b2805e","last_reissued_at":"2026-07-05T03:14:40.123666Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:14:40.123666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.07230","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":"2026-07-05T03:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lkLoNEEtCUFXhv6yDQLwgj2bzJzn9DXIMFLJQ0Z8wvKY+XdM6cleU4+eeVK04z1dLkDYE9L52WrabUWUQr6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:38:18.331945Z"},"content_sha256":"c7549513bbcfdf626488a75a2ff19381a184d88b89864db88ae93bcb4d514f36","schema_version":"1.0","event_id":"sha256:c7549513bbcfdf626488a75a2ff19381a184d88b89864db88ae93bcb4d514f36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:K6GIN7VUVBEJ2AS3YRZBW36LSE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Mathematical Properties of Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Kevin Knight, Maria Ryskina","submitted_at":"2021-09-15T11:54:28Z","abstract_excerpt":"Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.07230","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/2109.07230/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":"2026-07-05T03:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+IR3ZjfHPBzEI//F+4XgroasNyiBDwoirDE3YQojBPjp4ZXFavuNw4xsSGDLP66SSX9hnf1NIXolredQM68Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:38:18.332327Z"},"content_sha256":"016aa543cb43b9895dd3acad73773dc1d7b21bf3bfd751633d0b3bbe04604d60","schema_version":"1.0","event_id":"sha256:016aa543cb43b9895dd3acad73773dc1d7b21bf3bfd751633d0b3bbe04604d60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE/bundle.json","state_url":"https://pith.science/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE/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":"2026-07-07T13:38:18Z","links":{"resolver":"https://pith.science/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE","bundle":"https://pith.science/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE/bundle.json","state":"https://pith.science/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6GIN7VUVBEJ2AS3YRZBW36LSE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:K6GIN7VUVBEJ2AS3YRZBW36LSE","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":"380a485dc416612d8136fb926fdb0733941b89cf86fb438188afc2536329e913","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2021-09-15T11:54:28Z","title_canon_sha256":"73c8e8902f6cfe79612ef5c3444d0fc7bf3926c00311bc4c4acbcbd07a3ee8ad"},"schema_version":"1.0","source":{"id":"2109.07230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.07230","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"2109.07230v1","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.07230","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"K6GIN7VUVBEJ","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"pith_short_16","alias_value":"K6GIN7VUVBEJ2AS3","created_at":"2026-07-05T03:14:40Z"},{"alias_kind":"pith_short_8","alias_value":"K6GIN7VU","created_at":"2026-07-05T03:14:40Z"}],"graph_snapshots":[{"event_id":"sha256:016aa543cb43b9895dd3acad73773dc1d7b21bf3bfd751633d0b3bbe04604d60","target":"graph","created_at":"2026-07-05T03:14:40Z","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/2109.07230/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora.","authors_text":"Kevin Knight, Maria Ryskina","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2021-09-15T11:54:28Z","title":"Learning Mathematical Properties of Integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.07230","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:c7549513bbcfdf626488a75a2ff19381a184d88b89864db88ae93bcb4d514f36","target":"record","created_at":"2026-07-05T03:14:40Z","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":"380a485dc416612d8136fb926fdb0733941b89cf86fb438188afc2536329e913","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2021-09-15T11:54:28Z","title_canon_sha256":"73c8e8902f6cfe79612ef5c3444d0fc7bf3926c00311bc4c4acbcbd07a3ee8ad"},"schema_version":"1.0","source":{"id":"2109.07230","kind":"arxiv","version":1}},"canonical_sha256":"578c86feb4a8489d025bc4721b6fcb9102cb5f83df741a75529d0b86d6b2805e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"578c86feb4a8489d025bc4721b6fcb9102cb5f83df741a75529d0b86d6b2805e","first_computed_at":"2026-07-05T03:14:40.123666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:14:40.123666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fMTcJib8snDQBj1uRu6g+hOIadTAt8IZpU80ZC3MUUPCmhP53Eqe6niGzrKb700VzeRtzoUIopqv/juq6qmFDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:14:40.124014Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.07230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7549513bbcfdf626488a75a2ff19381a184d88b89864db88ae93bcb4d514f36","sha256:016aa543cb43b9895dd3acad73773dc1d7b21bf3bfd751633d0b3bbe04604d60"],"state_sha256":"afb61dc8839eccc82bf8e0fe49b6b75e42cf0b3cd8b5484207482adfe900c22c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cf74l4bat61sm0UbTZ5vTI8T/KViCDB4iOBXhT9m21/LfiiIaw+yGyLB1OMesQbU6dIcoYJpgy2DRJPQjaNUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:38:18.334223Z","bundle_sha256":"87e5ce917840c54ae5c80d425e3b02b552bddfd9c94c5d27c0ee144296a6c77f"}}