{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IUOQI7MWTDJ2CYORYAGAJORRMB","short_pith_number":"pith:IUOQI7MW","canonical_record":{"source":{"id":"1207.2170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2012-07-09T20:31:11Z","cross_cats_sorted":[],"title_canon_sha256":"fce3e3fbdb9e9a52d7913faafd2a3845df54d76a790730edcd77b14019b9da60","abstract_canon_sha256":"07762a4ff8c63ccb2419fd7f84352f7b206eaef4d576d28352119020e7ee0a23"},"schema_version":"1.0"},"canonical_sha256":"451d047d9698d3a161d1c00c04ba31605ea6b825c0d643a50831f31d2e1b5638","source":{"kind":"arxiv","id":"1207.2170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2170","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2170v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2170","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"IUOQI7MWTDJ2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IUOQI7MWTDJ2CYOR","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IUOQI7MW","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IUOQI7MWTDJ2CYORYAGAJORRMB","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2012-07-09T20:31:11Z","cross_cats_sorted":[],"title_canon_sha256":"fce3e3fbdb9e9a52d7913faafd2a3845df54d76a790730edcd77b14019b9da60","abstract_canon_sha256":"07762a4ff8c63ccb2419fd7f84352f7b206eaef4d576d28352119020e7ee0a23"},"schema_version":"1.0"},"canonical_sha256":"451d047d9698d3a161d1c00c04ba31605ea6b825c0d643a50831f31d2e1b5638","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:24.811990Z","signature_b64":"c7l9qmE+TmMHeIVrFEQmrTQkh8VnVtzc7uLYcb8dAWPgFbneVTsGAoar1dXi2bCfBCp68gs88wBofYEQfyoTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"451d047d9698d3a161d1c00c04ba31605ea6b825c0d643a50831f31d2e1b5638","last_reissued_at":"2026-05-18T03:51:24.811242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:24.811242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2170","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":"2026-05-18T03:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFZ/QPLDKlfvXqAJrjr1V+ysYkNm8nxNCvVnEy2UBHB+3LodVO7zPG9IyV9UWURt2aozlwmR28W83F3GvApRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:04:28.980215Z"},"content_sha256":"7d777e97be801574dbf6598ea4045ef1e67973a3482298c22f4d80d7b00f6d3e","schema_version":"1.0","event_id":"sha256:7d777e97be801574dbf6598ea4045ef1e67973a3482298c22f4d80d7b00f6d3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IUOQI7MWTDJ2CYORYAGAJORRMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Sumerian Words of Fractions in Babylonian Mathematics: igi-n-g\\'al and igi-te-en","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Kazuo Muroi","submitted_at":"2012-07-09T20:31:11Z","abstract_excerpt":"In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-g\\'al \"the reciprocal of (the number) n\", which is often abbreviated to igi-n, and igi-te-en whose meaning is somewhat abstract, that is, \"a proportion (of something)\" or \"the ratio (of something to another)\"(1). Thus the mathematical meanings of the two terms are quite clear, but we have not been able to clarify their literal meanings or their origins so far.\n  In the present paper I shall offer a most probable interpretation of the early term, igi-n-g\\'al, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2170","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":""},"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":"2026-05-18T03:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FtxU1FDtl2e/SZQEluP1JWBb591dJ2jr9Yzb0w26qogTF/Njde1oMUxEd/eDuD7AOsStoycpgb6mZusRD02zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:04:28.980946Z"},"content_sha256":"b18b7a8509bd15c029977e0cd3baead2847f8e6a16b7278f00dcdb20862204b1","schema_version":"1.0","event_id":"sha256:b18b7a8509bd15c029977e0cd3baead2847f8e6a16b7278f00dcdb20862204b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUOQI7MWTDJ2CYORYAGAJORRMB/bundle.json","state_url":"https://pith.science/pith/IUOQI7MWTDJ2CYORYAGAJORRMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUOQI7MWTDJ2CYORYAGAJORRMB/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":"2026-06-11T06:04:28Z","links":{"resolver":"https://pith.science/pith/IUOQI7MWTDJ2CYORYAGAJORRMB","bundle":"https://pith.science/pith/IUOQI7MWTDJ2CYORYAGAJORRMB/bundle.json","state":"https://pith.science/pith/IUOQI7MWTDJ2CYORYAGAJORRMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUOQI7MWTDJ2CYORYAGAJORRMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IUOQI7MWTDJ2CYORYAGAJORRMB","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":"07762a4ff8c63ccb2419fd7f84352f7b206eaef4d576d28352119020e7ee0a23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2012-07-09T20:31:11Z","title_canon_sha256":"fce3e3fbdb9e9a52d7913faafd2a3845df54d76a790730edcd77b14019b9da60"},"schema_version":"1.0","source":{"id":"1207.2170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2170","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2170v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2170","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"IUOQI7MWTDJ2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IUOQI7MWTDJ2CYOR","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IUOQI7MW","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:b18b7a8509bd15c029977e0cd3baead2847f8e6a16b7278f00dcdb20862204b1","target":"graph","created_at":"2026-05-18T03:51:24Z","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"},"paper":{"abstract_excerpt":"In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-g\\'al \"the reciprocal of (the number) n\", which is often abbreviated to igi-n, and igi-te-en whose meaning is somewhat abstract, that is, \"a proportion (of something)\" or \"the ratio (of something to another)\"(1). Thus the mathematical meanings of the two terms are quite clear, but we have not been able to clarify their literal meanings or their origins so far.\n  In the present paper I shall offer a most probable interpretation of the early term, igi-n-g\\'al, and","authors_text":"Kazuo Muroi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2012-07-09T20:31:11Z","title":"Two Sumerian Words of Fractions in Babylonian Mathematics: igi-n-g\\'al and igi-te-en"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2170","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":"sha256:7d777e97be801574dbf6598ea4045ef1e67973a3482298c22f4d80d7b00f6d3e","target":"record","created_at":"2026-05-18T03:51:24Z","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":"07762a4ff8c63ccb2419fd7f84352f7b206eaef4d576d28352119020e7ee0a23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2012-07-09T20:31:11Z","title_canon_sha256":"fce3e3fbdb9e9a52d7913faafd2a3845df54d76a790730edcd77b14019b9da60"},"schema_version":"1.0","source":{"id":"1207.2170","kind":"arxiv","version":1}},"canonical_sha256":"451d047d9698d3a161d1c00c04ba31605ea6b825c0d643a50831f31d2e1b5638","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"451d047d9698d3a161d1c00c04ba31605ea6b825c0d643a50831f31d2e1b5638","first_computed_at":"2026-05-18T03:51:24.811242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:24.811242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c7l9qmE+TmMHeIVrFEQmrTQkh8VnVtzc7uLYcb8dAWPgFbneVTsGAoar1dXi2bCfBCp68gs88wBofYEQfyoTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:24.811990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d777e97be801574dbf6598ea4045ef1e67973a3482298c22f4d80d7b00f6d3e","sha256:b18b7a8509bd15c029977e0cd3baead2847f8e6a16b7278f00dcdb20862204b1"],"state_sha256":"2b2aefd1204ebac4d6c2b141bdd268abe758fd53ac428d349bb8ad89bb57e379"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u4dmJneEdEXOcvQ99C/rBHqCxqbb4UmxHMqorOfV6THZ3cjT+RTHNeE4VMIIC/ctqc9dTPRmoOOVR3LfGxUfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:04:28.983518Z","bundle_sha256":"83b690953487e03f9e9f3f11d4cc43a6386547e9a54063517979ca94a70e2213"}}