{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:GRYIU6HQ3DVUS3KPQFF5C5BHSP","short_pith_number":"pith:GRYIU6HQ","canonical_record":{"source":{"id":"2106.05621","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2021-06-10T10:00:51Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"169add3a49b9b98a693d60315a412fa6187292c45b28781fc60829d45f70c08f","abstract_canon_sha256":"b4169361ee51eaadd9517571bbf1c25949eade2ac098afd27d3bbf5295d70dd4"},"schema_version":"1.0"},"canonical_sha256":"34708a78f0d8eb496d4f814bd1742793e3af494bb0a946b7ee6ef9a05da96375","source":{"kind":"arxiv","id":"2106.05621","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05621","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05621v3","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05621","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"GRYIU6HQ3DVU","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"pith_short_16","alias_value":"GRYIU6HQ3DVUS3KP","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"pith_short_8","alias_value":"GRYIU6HQ","created_at":"2026-07-05T04:22:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:GRYIU6HQ3DVUS3KPQFF5C5BHSP","target":"record","payload":{"canonical_record":{"source":{"id":"2106.05621","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2021-06-10T10:00:51Z","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"title_canon_sha256":"169add3a49b9b98a693d60315a412fa6187292c45b28781fc60829d45f70c08f","abstract_canon_sha256":"b4169361ee51eaadd9517571bbf1c25949eade2ac098afd27d3bbf5295d70dd4"},"schema_version":"1.0"},"canonical_sha256":"34708a78f0d8eb496d4f814bd1742793e3af494bb0a946b7ee6ef9a05da96375","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:22:50.940763Z","signature_b64":"mjO/leAYB5NY/PStKaKpX+9r5P+06igWZA49fHPmCSeli1TR9CDXoyzh/F6KuHVQZIHPWaIJIsG2v7Kj7UB+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34708a78f0d8eb496d4f814bd1742793e3af494bb0a946b7ee6ef9a05da96375","last_reissued_at":"2026-07-05T04:22:50.940228Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:22:50.940228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.05621","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGmPQeGvDQOT9UmG4gBtk88SKd5YzHM32NrkVHmjw4hynoGioNfs5LmGXYYYgY28cniVHQWDtDmtlc9KjErgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:43:59.341204Z"},"content_sha256":"a5f165dd340eb1ed5b2b6439774f94ab21b960cefdc8a58d531fb7ca86cb011a","schema_version":"1.0","event_id":"sha256:a5f165dd340eb1ed5b2b6439774f94ab21b960cefdc8a58d531fb7ca86cb011a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:GRYIU6HQ3DVUS3KPQFF5C5BHSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rationalizability of field extensions with a view towards Feynman integrals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"primary_cat":"math.AC","authors_text":"Andreas Hochenegger, Dino Festi","submitted_at":"2021-06-10T10:00:51Z","abstract_excerpt":"In 2021, Marco Besier and the first author introduced the concept of rationalizability of square roots to simplify arguments of Feynman integrals. In this work, we generalize the definition of rationalizability to field extensions. We then show that the rationalizability of a set of quadratic field extensions is equivalent to the rationalizability of the compositum of the field extensions, providing a new strategy to prove rationalizability of sets of square roots of polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05621","kind":"arxiv","version":3},"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/2106.05621/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":"2026-07-05T04:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4flHjPWt80s9CwmbxnsLJkHampNyjufxHT7NWza7S5t4Aek8qFAFJmI0Ci0/A2q9VWuAWPiexVswcaE4QKoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:43:59.341823Z"},"content_sha256":"9b718c97999b8c8d5d505af397ed17663db0132d8a172d45e75a6c2d8910a2e8","schema_version":"1.0","event_id":"sha256:9b718c97999b8c8d5d505af397ed17663db0132d8a172d45e75a6c2d8910a2e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP/bundle.json","state_url":"https://pith.science/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP/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":"2026-08-03T21:43:59Z","links":{"resolver":"https://pith.science/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP","bundle":"https://pith.science/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP/bundle.json","state":"https://pith.science/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRYIU6HQ3DVUS3KPQFF5C5BHSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GRYIU6HQ3DVUS3KPQFF5C5BHSP","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":"b4169361ee51eaadd9517571bbf1c25949eade2ac098afd27d3bbf5295d70dd4","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2021-06-10T10:00:51Z","title_canon_sha256":"169add3a49b9b98a693d60315a412fa6187292c45b28781fc60829d45f70c08f"},"schema_version":"1.0","source":{"id":"2106.05621","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05621","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05621v3","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05621","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"GRYIU6HQ3DVU","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"pith_short_16","alias_value":"GRYIU6HQ3DVUS3KP","created_at":"2026-07-05T04:22:50Z"},{"alias_kind":"pith_short_8","alias_value":"GRYIU6HQ","created_at":"2026-07-05T04:22:50Z"}],"graph_snapshots":[{"event_id":"sha256:9b718c97999b8c8d5d505af397ed17663db0132d8a172d45e75a6c2d8910a2e8","target":"graph","created_at":"2026-07-05T04:22:50Z","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/2106.05621/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 2021, Marco Besier and the first author introduced the concept of rationalizability of square roots to simplify arguments of Feynman integrals. In this work, we generalize the definition of rationalizability to field extensions. We then show that the rationalizability of a set of quadratic field extensions is equivalent to the rationalizability of the compositum of the field extensions, providing a new strategy to prove rationalizability of sets of square roots of polynomials.","authors_text":"Andreas Hochenegger, Dino Festi","cross_cats":["hep-th","math-ph","math.AG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2021-06-10T10:00:51Z","title":"Rationalizability of field extensions with a view towards Feynman integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05621","kind":"arxiv","version":3},"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:a5f165dd340eb1ed5b2b6439774f94ab21b960cefdc8a58d531fb7ca86cb011a","target":"record","created_at":"2026-07-05T04:22:50Z","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":"b4169361ee51eaadd9517571bbf1c25949eade2ac098afd27d3bbf5295d70dd4","cross_cats_sorted":["hep-th","math-ph","math.AG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2021-06-10T10:00:51Z","title_canon_sha256":"169add3a49b9b98a693d60315a412fa6187292c45b28781fc60829d45f70c08f"},"schema_version":"1.0","source":{"id":"2106.05621","kind":"arxiv","version":3}},"canonical_sha256":"34708a78f0d8eb496d4f814bd1742793e3af494bb0a946b7ee6ef9a05da96375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34708a78f0d8eb496d4f814bd1742793e3af494bb0a946b7ee6ef9a05da96375","first_computed_at":"2026-07-05T04:22:50.940228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:22:50.940228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mjO/leAYB5NY/PStKaKpX+9r5P+06igWZA49fHPmCSeli1TR9CDXoyzh/F6KuHVQZIHPWaIJIsG2v7Kj7UB+BA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:22:50.940763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.05621","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5f165dd340eb1ed5b2b6439774f94ab21b960cefdc8a58d531fb7ca86cb011a","sha256:9b718c97999b8c8d5d505af397ed17663db0132d8a172d45e75a6c2d8910a2e8"],"state_sha256":"1624014180d4ea6dccc4f727b5355575e7d79cd71ce45eeec8e8f9585fb68f98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjeVN2uXThrN9b5gPxF11IqE0/JSrpiZ9eJhQYQXi0Tsu6nyvbK/lJC0fNBw5kKoj16oFG1GkWFT7aW/dX+4Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:43:59.347168Z","bundle_sha256":"074773ab308afb017b5ee5adce268f2eb239f01ed86957394e13d74d67f86e3a"}}