{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CRVBSYPKSMQPAQI2ZWW6VDINBW","short_pith_number":"pith:CRVBSYPK","canonical_record":{"source":{"id":"2109.09301","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2021-09-20T05:22:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c244a2f70f6439621327b479945d49ba6de29aaac13a57e945a139f65f6154b7","abstract_canon_sha256":"6f52ac6411462bdd5d6b01c5cd6fa62edfb6622ad13b3f45cf480d9b838d5532"},"schema_version":"1.0"},"canonical_sha256":"146a1961ea9320f0411acdadea8d0d0dbd3f36c92cf1dd0fe22d666354bf19c3","source":{"kind":"arxiv","id":"2109.09301","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.09301","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"2109.09301v3","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.09301","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"CRVBSYPKSMQP","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"pith_short_16","alias_value":"CRVBSYPKSMQPAQI2","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"pith_short_8","alias_value":"CRVBSYPK","created_at":"2026-07-05T08:27:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CRVBSYPKSMQPAQI2ZWW6VDINBW","target":"record","payload":{"canonical_record":{"source":{"id":"2109.09301","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2021-09-20T05:22:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c244a2f70f6439621327b479945d49ba6de29aaac13a57e945a139f65f6154b7","abstract_canon_sha256":"6f52ac6411462bdd5d6b01c5cd6fa62edfb6622ad13b3f45cf480d9b838d5532"},"schema_version":"1.0"},"canonical_sha256":"146a1961ea9320f0411acdadea8d0d0dbd3f36c92cf1dd0fe22d666354bf19c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:27:39.054005Z","signature_b64":"HjOhXwkk+4UW0t4w+fvB4/NUWRAWnMsc22OlgwpzwhA7nXvX/ROsV/hR6fds3o2uVbakkXjGNr8IHMY9okmqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"146a1961ea9320f0411acdadea8d0d0dbd3f36c92cf1dd0fe22d666354bf19c3","last_reissued_at":"2026-07-05T08:27:39.053581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:27:39.053581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.09301","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":"2026-07-05T08:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8BfmCPvJ1s7Z4ihYhYWimSMupPJNc8icjzyKoKHkpOnPU0/KeohC67WB0Im3u68srcrTMHmPO/Zcj0pVPeTLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T09:42:57.574886Z"},"content_sha256":"cb374bf9adc1d24dd5b4411a24b8fbb66a6fc469506fb9a4a4f072612ab42ce1","schema_version":"1.0","event_id":"sha256:cb374bf9adc1d24dd5b4411a24b8fbb66a6fc469506fb9a4a4f072612ab42ce1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CRVBSYPKSMQPAQI2ZWW6VDINBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality of the Galois action on the fundamental group of $\\mathbb{P}^1\\setminus\\{0,1,\\infty\\}$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alexander Petrov","submitted_at":"2021-09-20T05:22:28Z","abstract_excerpt":"We prove that any semi-simple representation of the Galois group of a number field coming from geometry appears as a subquotient of the ring of regular functions on the pro-algebraic completion of the fundamental group of the projective line with $3$ punctures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.09301","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/2109.09301/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":"2026-07-05T08:27:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7JufN9YYKHo2z/TSJTr4rD+ActexGgKFYFJ3oDull8ab4V0SfY4txLVo1iB6D+HJVaSfysoMW+jNoSdXQwk4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T09:42:57.575410Z"},"content_sha256":"df73dc237fddb6e1ed36d29a9e019053d8616b2ab0548b82ed6e1add2050f628","schema_version":"1.0","event_id":"sha256:df73dc237fddb6e1ed36d29a9e019053d8616b2ab0548b82ed6e1add2050f628"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW/bundle.json","state_url":"https://pith.science/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW/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":"2026-08-22T09:42:57Z","links":{"resolver":"https://pith.science/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW","bundle":"https://pith.science/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW/bundle.json","state":"https://pith.science/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRVBSYPKSMQPAQI2ZWW6VDINBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CRVBSYPKSMQPAQI2ZWW6VDINBW","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":"6f52ac6411462bdd5d6b01c5cd6fa62edfb6622ad13b3f45cf480d9b838d5532","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2021-09-20T05:22:28Z","title_canon_sha256":"c244a2f70f6439621327b479945d49ba6de29aaac13a57e945a139f65f6154b7"},"schema_version":"1.0","source":{"id":"2109.09301","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.09301","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"arxiv_version","alias_value":"2109.09301v3","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.09301","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"pith_short_12","alias_value":"CRVBSYPKSMQP","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"pith_short_16","alias_value":"CRVBSYPKSMQPAQI2","created_at":"2026-07-05T08:27:39Z"},{"alias_kind":"pith_short_8","alias_value":"CRVBSYPK","created_at":"2026-07-05T08:27:39Z"}],"graph_snapshots":[{"event_id":"sha256:df73dc237fddb6e1ed36d29a9e019053d8616b2ab0548b82ed6e1add2050f628","target":"graph","created_at":"2026-07-05T08:27:39Z","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/2109.09301/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that any semi-simple representation of the Galois group of a number field coming from geometry appears as a subquotient of the ring of regular functions on the pro-algebraic completion of the fundamental group of the projective line with $3$ punctures.","authors_text":"Alexander Petrov","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2021-09-20T05:22:28Z","title":"Universality of the Galois action on the fundamental group of $\\mathbb{P}^1\\setminus\\{0,1,\\infty\\}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.09301","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:cb374bf9adc1d24dd5b4411a24b8fbb66a6fc469506fb9a4a4f072612ab42ce1","target":"record","created_at":"2026-07-05T08:27:39Z","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":"6f52ac6411462bdd5d6b01c5cd6fa62edfb6622ad13b3f45cf480d9b838d5532","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2021-09-20T05:22:28Z","title_canon_sha256":"c244a2f70f6439621327b479945d49ba6de29aaac13a57e945a139f65f6154b7"},"schema_version":"1.0","source":{"id":"2109.09301","kind":"arxiv","version":3}},"canonical_sha256":"146a1961ea9320f0411acdadea8d0d0dbd3f36c92cf1dd0fe22d666354bf19c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"146a1961ea9320f0411acdadea8d0d0dbd3f36c92cf1dd0fe22d666354bf19c3","first_computed_at":"2026-07-05T08:27:39.053581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:39.053581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HjOhXwkk+4UW0t4w+fvB4/NUWRAWnMsc22OlgwpzwhA7nXvX/ROsV/hR6fds3o2uVbakkXjGNr8IHMY9okmqBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:39.054005Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.09301","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb374bf9adc1d24dd5b4411a24b8fbb66a6fc469506fb9a4a4f072612ab42ce1","sha256:df73dc237fddb6e1ed36d29a9e019053d8616b2ab0548b82ed6e1add2050f628"],"state_sha256":"7667fd16d4ad278b4c7462aca6e206451c455ff882c97f7acea23069c58d2f17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E62sVeAOsQKTCokRSqYG9JBZbJNDTXWAIUCBX2Gh2LKPfypG/WIypN/tWgNOgDNz+AjnymhfXTAC937lBi3kCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T09:42:57.580376Z","bundle_sha256":"2a92dd401d5629181d9834337cb52d49e7490482f1c24fa589106a327029015d"}}