{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3JOP7O7JMR6ANPQIRIZLT2X5HY","short_pith_number":"pith:3JOP7O7J","canonical_record":{"source":{"id":"1709.05959","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2017-09-15T07:54:45Z","cross_cats_sorted":[],"title_canon_sha256":"034dc636ee3c52a3525cd114e4f78c9168cd5ae773098e15c15a629f6acfcb6d","abstract_canon_sha256":"62d0ae7ab865b44131ceb15526c649834884446c7e8366a9f5e4f1584eaa246f"},"schema_version":"1.0"},"canonical_sha256":"da5cffbbe9647c06be088a32b9eafd3e33eac458c3a8dd94bc52b3460f38f93e","source":{"kind":"arxiv","id":"1709.05959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05959","created_at":"2026-05-18T00:34:58Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05959v1","created_at":"2026-05-18T00:34:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05959","created_at":"2026-05-18T00:34:58Z"},{"alias_kind":"pith_short_12","alias_value":"3JOP7O7JMR6A","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3JOP7O7JMR6ANPQI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3JOP7O7J","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3JOP7O7JMR6ANPQIRIZLT2X5HY","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05959","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2017-09-15T07:54:45Z","cross_cats_sorted":[],"title_canon_sha256":"034dc636ee3c52a3525cd114e4f78c9168cd5ae773098e15c15a629f6acfcb6d","abstract_canon_sha256":"62d0ae7ab865b44131ceb15526c649834884446c7e8366a9f5e4f1584eaa246f"},"schema_version":"1.0"},"canonical_sha256":"da5cffbbe9647c06be088a32b9eafd3e33eac458c3a8dd94bc52b3460f38f93e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:58.684090Z","signature_b64":"uU42v+VOVHgnVCo9Yc3ARsNUi7t5etbvUy7Aydg+Qlyc5bzudrD1Fb2RpjG3l2CiPxQezKjJG5F7iRWJw6K6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da5cffbbe9647c06be088a32b9eafd3e33eac458c3a8dd94bc52b3460f38f93e","last_reissued_at":"2026-05-18T00:34:58.683286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:58.683286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05959","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":"2026-05-18T00:34:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pn8AsYVsEhxWrSOw/QRWU9fxIJcm6xYz4yrmLUiG1WG1Kl0m8IfN0pWHu99Ie/RtlQY+gvXFSyaqha5v5qFaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:28:23.829555Z"},"content_sha256":"d31b74028ca849b5b0c24f94380c9610073c59c65f8d575f83ad9d413aeecdd0","schema_version":"1.0","event_id":"sha256:d31b74028ca849b5b0c24f94380c9610073c59c65f8d575f83ad9d413aeecdd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3JOP7O7JMR6ANPQIRIZLT2X5HY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Algebraic Number Theory, Part I: Foundations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Joram Soch","submitted_at":"2017-09-15T07:54:45Z","abstract_excerpt":"We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space, therefore replaces multiplication with addition and allows to capture variation in the natural numbers from variation in the prime numbers. This automatically puts prime numbers to their designated place of atomic particles of natural numbers and enables fruitful new formulations of number-theoretic functions. We outline the theory, derive some basic results, mak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05959","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":"2026-05-18T00:34:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CD/6Vu+uoQffWlo4JVq55Eyvb9lUrbbpqHV06gWk8SPwZRGaDiiGDhaYePpzt5X14S022gMAR5H1/G0cIoUHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:28:23.829903Z"},"content_sha256":"feb635a478dc1d84c64383d31b81cdbef0f6fb768d0a1e9c791cdad682975328","schema_version":"1.0","event_id":"sha256:feb635a478dc1d84c64383d31b81cdbef0f6fb768d0a1e9c791cdad682975328"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY/bundle.json","state_url":"https://pith.science/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY/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":"2026-06-26T10:28:23Z","links":{"resolver":"https://pith.science/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY","bundle":"https://pith.science/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY/bundle.json","state":"https://pith.science/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JOP7O7JMR6ANPQIRIZLT2X5HY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3JOP7O7JMR6ANPQIRIZLT2X5HY","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":"62d0ae7ab865b44131ceb15526c649834884446c7e8366a9f5e4f1584eaa246f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2017-09-15T07:54:45Z","title_canon_sha256":"034dc636ee3c52a3525cd114e4f78c9168cd5ae773098e15c15a629f6acfcb6d"},"schema_version":"1.0","source":{"id":"1709.05959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05959","created_at":"2026-05-18T00:34:58Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05959v1","created_at":"2026-05-18T00:34:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05959","created_at":"2026-05-18T00:34:58Z"},{"alias_kind":"pith_short_12","alias_value":"3JOP7O7JMR6A","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3JOP7O7JMR6ANPQI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3JOP7O7J","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:feb635a478dc1d84c64383d31b81cdbef0f6fb768d0a1e9c791cdad682975328","target":"graph","created_at":"2026-05-18T00:34:58Z","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":"We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space, therefore replaces multiplication with addition and allows to capture variation in the natural numbers from variation in the prime numbers. This automatically puts prime numbers to their designated place of atomic particles of natural numbers and enables fruitful new formulations of number-theoretic functions. We outline the theory, derive some basic results, mak","authors_text":"Joram Soch","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2017-09-15T07:54:45Z","title":"Linear Algebraic Number Theory, Part I: Foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05959","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:d31b74028ca849b5b0c24f94380c9610073c59c65f8d575f83ad9d413aeecdd0","target":"record","created_at":"2026-05-18T00:34:58Z","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":"62d0ae7ab865b44131ceb15526c649834884446c7e8366a9f5e4f1584eaa246f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2017-09-15T07:54:45Z","title_canon_sha256":"034dc636ee3c52a3525cd114e4f78c9168cd5ae773098e15c15a629f6acfcb6d"},"schema_version":"1.0","source":{"id":"1709.05959","kind":"arxiv","version":1}},"canonical_sha256":"da5cffbbe9647c06be088a32b9eafd3e33eac458c3a8dd94bc52b3460f38f93e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da5cffbbe9647c06be088a32b9eafd3e33eac458c3a8dd94bc52b3460f38f93e","first_computed_at":"2026-05-18T00:34:58.683286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:58.683286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uU42v+VOVHgnVCo9Yc3ARsNUi7t5etbvUy7Aydg+Qlyc5bzudrD1Fb2RpjG3l2CiPxQezKjJG5F7iRWJw6K6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:58.684090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d31b74028ca849b5b0c24f94380c9610073c59c65f8d575f83ad9d413aeecdd0","sha256:feb635a478dc1d84c64383d31b81cdbef0f6fb768d0a1e9c791cdad682975328"],"state_sha256":"cf13c25cc511c61d4a659f6d0947fa7c0753d5ea00f6ae98bc4271f0b7ffc010"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4nFa8hboXar2cpHehN9dvwx1aS92c84jkIpABBlDL/qHzbF8uzZyvLL+Uius6HvNRFdxgX8G+sfcxW6AwKmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:28:23.831817Z","bundle_sha256":"2d978acfbe35c7315134c4aab3e706066b23697f19e6d292447bae3769ec63e5"}}