{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:JHPJX2GDYAIZUU45PSF6KPG6PI","short_pith_number":"pith:JHPJX2GD","canonical_record":{"source":{"id":"2211.16698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-11-30T02:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"96d47c3ee6b88629053d243a741a6ca2e308cc8c4fda69e4123eab7b769822f3","abstract_canon_sha256":"420711c1ffe7181a7b12c4bd373892363e742a2b3293d55aaa0774b3a6ff5dac"},"schema_version":"1.0"},"canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","source":{"kind":"arxiv","id":"2211.16698","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.16698","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"2211.16698v1","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16698","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"JHPJX2GDYAIZ","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"pith_short_16","alias_value":"JHPJX2GDYAIZUU45","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"pith_short_8","alias_value":"JHPJX2GD","created_at":"2026-07-05T05:21:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:JHPJX2GDYAIZUU45PSF6KPG6PI","target":"record","payload":{"canonical_record":{"source":{"id":"2211.16698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-11-30T02:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"96d47c3ee6b88629053d243a741a6ca2e308cc8c4fda69e4123eab7b769822f3","abstract_canon_sha256":"420711c1ffe7181a7b12c4bd373892363e742a2b3293d55aaa0774b3a6ff5dac"},"schema_version":"1.0"},"canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:21:09.895472Z","signature_b64":"Gf3wmPca+p/hg+9c6kPDjfGt8Bhbbchttbol+KGyCRMlW/8bjXCvJiU58gHZev4JjoWumXjeQIJbCZL+tnXYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","last_reissued_at":"2026-07-05T05:21:09.894981Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:21:09.894981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.16698","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":"2026-07-05T05:21:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X8kzffuWkwOKffHl39lcuHAJ6TLZcp2hO0UxhNDXjdq6CJh8OFOzYdR3OFRMG0xUVSUuQGCHBFFTNmlf2Y9pAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:56:14.906206Z"},"content_sha256":"c95a6aaafa08bf78d31ccfa1c11314844281a96a5921b9129feb5f98fe3c0fb7","schema_version":"1.0","event_id":"sha256:c95a6aaafa08bf78d31ccfa1c11314844281a96a5921b9129feb5f98fe3c0fb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:JHPJX2GDYAIZUU45PSF6KPG6PI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Malle's conjecture with multiple invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabian Gundlach","submitted_at":"2022-11-30T02:39:53Z","abstract_excerpt":"We define invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the number of extensions that satisfy $\\operatorname{inv}_i\\leq X_i$ for all $X_i$. The resulting conjecture is proved for abelian Galois groups. We also describe refined Artin conductors that carry essentially the same information as the invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16698","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/2211.16698/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":"2026-07-05T05:21:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kzdkTOXqkDmevkYB0PbDAcUWnI43FBbdHSEEcJMS3lUkGKoCAqhK5LpZsUIP95Tt5eD02AaCRi9rnVbcRMRiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:56:14.906723Z"},"content_sha256":"6015e8453880a9479e0378558da5d6c5f6bf3857827b8c730d58a6e2d7809918","schema_version":"1.0","event_id":"sha256:6015e8453880a9479e0378558da5d6c5f6bf3857827b8c730d58a6e2d7809918"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/bundle.json","state_url":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/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":"2026-08-08T21:56:14Z","links":{"resolver":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI","bundle":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/bundle.json","state":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JHPJX2GDYAIZUU45PSF6KPG6PI","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":"420711c1ffe7181a7b12c4bd373892363e742a2b3293d55aaa0774b3a6ff5dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-11-30T02:39:53Z","title_canon_sha256":"96d47c3ee6b88629053d243a741a6ca2e308cc8c4fda69e4123eab7b769822f3"},"schema_version":"1.0","source":{"id":"2211.16698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.16698","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"2211.16698v1","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16698","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"JHPJX2GDYAIZ","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"pith_short_16","alias_value":"JHPJX2GDYAIZUU45","created_at":"2026-07-05T05:21:09Z"},{"alias_kind":"pith_short_8","alias_value":"JHPJX2GD","created_at":"2026-07-05T05:21:09Z"}],"graph_snapshots":[{"event_id":"sha256:6015e8453880a9479e0378558da5d6c5f6bf3857827b8c730d58a6e2d7809918","target":"graph","created_at":"2026-07-05T05:21:09Z","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/2211.16698/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the number of extensions that satisfy $\\operatorname{inv}_i\\leq X_i$ for all $X_i$. The resulting conjecture is proved for abelian Galois groups. We also describe refined Artin conductors that carry essentially the same information as the invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$.","authors_text":"Fabian Gundlach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-11-30T02:39:53Z","title":"Malle's conjecture with multiple invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16698","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:c95a6aaafa08bf78d31ccfa1c11314844281a96a5921b9129feb5f98fe3c0fb7","target":"record","created_at":"2026-07-05T05:21:09Z","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":"420711c1ffe7181a7b12c4bd373892363e742a2b3293d55aaa0774b3a6ff5dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-11-30T02:39:53Z","title_canon_sha256":"96d47c3ee6b88629053d243a741a6ca2e308cc8c4fda69e4123eab7b769822f3"},"schema_version":"1.0","source":{"id":"2211.16698","kind":"arxiv","version":1}},"canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","first_computed_at":"2026-07-05T05:21:09.894981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:21:09.894981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gf3wmPca+p/hg+9c6kPDjfGt8Bhbbchttbol+KGyCRMlW/8bjXCvJiU58gHZev4JjoWumXjeQIJbCZL+tnXYDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:21:09.895472Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.16698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c95a6aaafa08bf78d31ccfa1c11314844281a96a5921b9129feb5f98fe3c0fb7","sha256:6015e8453880a9479e0378558da5d6c5f6bf3857827b8c730d58a6e2d7809918"],"state_sha256":"02b9a251fd1ddd7f931ef5edbcf8c725f8da91e9a6731933b8ae30b650c3a0e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Jn+qbm9NPf174qUcZj9ZHb0BMiLSTuJh5NVV2muU8lhuhON4VpSxOGFI2BW2u4ojeLktCug/JgsdvnFa8upDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T21:56:14.911603Z","bundle_sha256":"924c90a62ce4b0d0ebe48cb380014e3dbbed0a7fce03ac8ab30b4adfd09d9773"}}