{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:OOSS4HOUOHK4SWTJBZY7WSHQ4H","short_pith_number":"pith:OOSS4HOU","canonical_record":{"source":{"id":"0906.2925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-16T13:10:18Z","cross_cats_sorted":["cs.SC","math.AC"],"title_canon_sha256":"4f042474c857772325c49dda748db1d8e3bca6348a03ddd4da8b9afe00bfe982","abstract_canon_sha256":"88716d6d94317ab3a9240b12fadceef270c766cbff60092c7f3367d9a66190c3"},"schema_version":"1.0"},"canonical_sha256":"73a52e1dd471d5c95a690e71fb48f0e1c5c8f15b544d54a1c3627c4eae2ebe44","source":{"kind":"arxiv","id":"0906.2925","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2925","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2925v1","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2925","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"OOSS4HOUOHK4","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"pith_short_16","alias_value":"OOSS4HOUOHK4SWTJ","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"pith_short_8","alias_value":"OOSS4HOU","created_at":"2026-07-04T15:43:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:OOSS4HOUOHK4SWTJBZY7WSHQ4H","target":"record","payload":{"canonical_record":{"source":{"id":"0906.2925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-16T13:10:18Z","cross_cats_sorted":["cs.SC","math.AC"],"title_canon_sha256":"4f042474c857772325c49dda748db1d8e3bca6348a03ddd4da8b9afe00bfe982","abstract_canon_sha256":"88716d6d94317ab3a9240b12fadceef270c766cbff60092c7f3367d9a66190c3"},"schema_version":"1.0"},"canonical_sha256":"73a52e1dd471d5c95a690e71fb48f0e1c5c8f15b544d54a1c3627c4eae2ebe44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:43:54.684423Z","signature_b64":"QJVGFsOTc2/P5UESHPKwdjwyXV7R0VxctwSrXf2tKspM46woM4NkxhMhAKBgCWlShWlLDNBI/p2r9y9ExwHICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73a52e1dd471d5c95a690e71fb48f0e1c5c8f15b544d54a1c3627c4eae2ebe44","last_reissued_at":"2026-07-04T15:43:54.683995Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:43:54.683995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.2925","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":"2026-07-04T15:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hFebciTHUISS6aNwB8fgmIaxnxiaF5vngiXC9mXsSzfipbmH8ZlVMuI51SCeZegZQQwxYKyTW47pNsbiGWniCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:38:03.094025Z"},"content_sha256":"9e6559f2709eb3a4c0071cab7ff4c362cdb895e6ac767e243fba665004039b64","schema_version":"1.0","event_id":"sha256:9e6559f2709eb3a4c0071cab7ff4c362cdb895e6ac767e243fba665004039b64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:OOSS4HOUOHK4SWTJBZY7WSHQ4H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noether's forms for the study of non-composite rational functions and their spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.AC"],"primary_cat":"math.NT","authors_text":"Guillaume Ch\\`eze (IMT), Laurent Bus\\'e (INRIA Sophia Antipolis), Salah Najib (MPI-MIS)","submitted_at":"2009-06-16T13:10:18Z","abstract_excerpt":"In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach, some new effective results are obtained. In particular, we show that the reduction modulo p of the spectrum of a given integer multivariate rational function r coincides with the spectrum of the reduction of r modulo p for p a prime integer greater or equal to an explicit bound. This bound is given in terms of the degree, the height and the number of variables of r. With the same strategy, we also st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2925","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/0906.2925/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":"2026-07-04T15:43:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AODaYvWNolR4XTqFp58nRuU+YJjLZA/XBVonWkq9E0kCpxKr352QEz9mv/VQXCFkLDBEgjC5aexSW1x8O6pUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:38:03.094622Z"},"content_sha256":"6dd5964e278c53c59cb4712253ffa3e48c65d0bb946e3419134aa1ddb868f020","schema_version":"1.0","event_id":"sha256:6dd5964e278c53c59cb4712253ffa3e48c65d0bb946e3419134aa1ddb868f020"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H/bundle.json","state_url":"https://pith.science/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H/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":"2026-07-05T05:38:03Z","links":{"resolver":"https://pith.science/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H","bundle":"https://pith.science/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H/bundle.json","state":"https://pith.science/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOSS4HOUOHK4SWTJBZY7WSHQ4H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OOSS4HOUOHK4SWTJBZY7WSHQ4H","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":"88716d6d94317ab3a9240b12fadceef270c766cbff60092c7f3367d9a66190c3","cross_cats_sorted":["cs.SC","math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-16T13:10:18Z","title_canon_sha256":"4f042474c857772325c49dda748db1d8e3bca6348a03ddd4da8b9afe00bfe982"},"schema_version":"1.0","source":{"id":"0906.2925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2925","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2925v1","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2925","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"OOSS4HOUOHK4","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"pith_short_16","alias_value":"OOSS4HOUOHK4SWTJ","created_at":"2026-07-04T15:43:54Z"},{"alias_kind":"pith_short_8","alias_value":"OOSS4HOU","created_at":"2026-07-04T15:43:54Z"}],"graph_snapshots":[{"event_id":"sha256:6dd5964e278c53c59cb4712253ffa3e48c65d0bb946e3419134aa1ddb868f020","target":"graph","created_at":"2026-07-04T15:43:54Z","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/0906.2925/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach, some new effective results are obtained. In particular, we show that the reduction modulo p of the spectrum of a given integer multivariate rational function r coincides with the spectrum of the reduction of r modulo p for p a prime integer greater or equal to an explicit bound. This bound is given in terms of the degree, the height and the number of variables of r. With the same strategy, we also st","authors_text":"Guillaume Ch\\`eze (IMT), Laurent Bus\\'e (INRIA Sophia Antipolis), Salah Najib (MPI-MIS)","cross_cats":["cs.SC","math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-16T13:10:18Z","title":"Noether's forms for the study of non-composite rational functions and their spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2925","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":"sha256:9e6559f2709eb3a4c0071cab7ff4c362cdb895e6ac767e243fba665004039b64","target":"record","created_at":"2026-07-04T15:43:54Z","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":"88716d6d94317ab3a9240b12fadceef270c766cbff60092c7f3367d9a66190c3","cross_cats_sorted":["cs.SC","math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-16T13:10:18Z","title_canon_sha256":"4f042474c857772325c49dda748db1d8e3bca6348a03ddd4da8b9afe00bfe982"},"schema_version":"1.0","source":{"id":"0906.2925","kind":"arxiv","version":1}},"canonical_sha256":"73a52e1dd471d5c95a690e71fb48f0e1c5c8f15b544d54a1c3627c4eae2ebe44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a52e1dd471d5c95a690e71fb48f0e1c5c8f15b544d54a1c3627c4eae2ebe44","first_computed_at":"2026-07-04T15:43:54.683995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:43:54.683995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QJVGFsOTc2/P5UESHPKwdjwyXV7R0VxctwSrXf2tKspM46woM4NkxhMhAKBgCWlShWlLDNBI/p2r9y9ExwHICQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:43:54.684423Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e6559f2709eb3a4c0071cab7ff4c362cdb895e6ac767e243fba665004039b64","sha256:6dd5964e278c53c59cb4712253ffa3e48c65d0bb946e3419134aa1ddb868f020"],"state_sha256":"9382f8297452d592dad00462cba7cd58ffec186d7e29fae86cf9581bc7d6bf2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6jvjwCnK5iuQqxSbD3aKNkDDx7+BJpK6JhEpRE/w13niYyeL+hErtvh/ioAMrSXxx1PIZfgIqi242Jyddk0dDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T05:38:03.096995Z","bundle_sha256":"695787d599be906682934b0c0f558c22c83343bbbb23e0706173cad7d5bb2bbd"}}