{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VKLYJQYNPHVT57ZSKCTRKG4F4K","short_pith_number":"pith:VKLYJQYN","canonical_record":{"source":{"id":"2507.05033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-07T14:16:54Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"712f201f466381e598d56a935587f6b2be36fa2be84e5b15292d97c26243f6ae","abstract_canon_sha256":"ac223c9a42bd61975c3086a9232411747cb37360c32228bfd35bc034e837500d"},"schema_version":"1.0"},"canonical_sha256":"aa9784c30d79eb3eff3250a7151b85e286c492038c76f841249dfc806b46a238","source":{"kind":"arxiv","id":"2507.05033","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05033","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05033v1","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05033","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"VKLYJQYNPHVT","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"pith_short_16","alias_value":"VKLYJQYNPHVT57ZS","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"pith_short_8","alias_value":"VKLYJQYN","created_at":"2026-07-05T11:33:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VKLYJQYNPHVT57ZSKCTRKG4F4K","target":"record","payload":{"canonical_record":{"source":{"id":"2507.05033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-07T14:16:54Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"712f201f466381e598d56a935587f6b2be36fa2be84e5b15292d97c26243f6ae","abstract_canon_sha256":"ac223c9a42bd61975c3086a9232411747cb37360c32228bfd35bc034e837500d"},"schema_version":"1.0"},"canonical_sha256":"aa9784c30d79eb3eff3250a7151b85e286c492038c76f841249dfc806b46a238","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:08.112018Z","signature_b64":"RUTh0xlXKQM/KC0a0iX3Ncxj6S0jVQFQfkYfbGL7lp9UWVeT3X2Sd1EwjjEPXA2+yAqRYM4oOHoWuH+dOuf2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa9784c30d79eb3eff3250a7151b85e286c492038c76f841249dfc806b46a238","last_reissued_at":"2026-07-05T11:33:08.111543Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:08.111543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.05033","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":"2026-07-05T11:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+mVUSVsPyyybzbUHBOEk7WOhyBZ+TPjL8UG27aJ5PEulSVQQ2o/UWFGW8lPE/SaPL4VC6+U0WW3iF5PxGWU7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:53:38.999589Z"},"content_sha256":"025267be7b87afa2cb9a6993705aea2eb042fe760c4edf43367b7f1c92477419","schema_version":"1.0","event_id":"sha256:025267be7b87afa2cb9a6993705aea2eb042fe760c4edf43367b7f1c92477419"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VKLYJQYNPHVT57ZSKCTRKG4F4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.DS","authors_text":"Dean Wardell, Mikhail Hlushchanka, Olga Lukina","submitted_at":"2025-07-07T14:16:54Z","abstract_excerpt":"In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute Galois groups of number fields into the automorphism group of a regular rooted tree. Our main result is that, for a degree 3 postcritically finite polynomial over a number field, where each finite postcritical point has at least one preimage outside the critical orbits, the associated profinite geometric iterated monodromy group is finitely invariably generated. Moreover, this group is determined by the isomorphism c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05033","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/2507.05033/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":"2026-07-05T11:33:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1HxXRYAwfd8eGR0/IeyjETNuUmzUuESOwHttJMZ5qSkNPxTA9dGsE0PB5lEP94DLG5baZQHqTFcWyL48FH+JBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:53:39.000137Z"},"content_sha256":"76b821c193aa01a6979036546ca3feed7169b2c2d99c50ebd08dda426fdd2b00","schema_version":"1.0","event_id":"sha256:76b821c193aa01a6979036546ca3feed7169b2c2d99c50ebd08dda426fdd2b00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K/bundle.json","state_url":"https://pith.science/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K/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":"2026-08-10T00:53:39Z","links":{"resolver":"https://pith.science/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K","bundle":"https://pith.science/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K/bundle.json","state":"https://pith.science/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKLYJQYNPHVT57ZSKCTRKG4F4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VKLYJQYNPHVT57ZSKCTRKG4F4K","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":"ac223c9a42bd61975c3086a9232411747cb37360c32228bfd35bc034e837500d","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-07T14:16:54Z","title_canon_sha256":"712f201f466381e598d56a935587f6b2be36fa2be84e5b15292d97c26243f6ae"},"schema_version":"1.0","source":{"id":"2507.05033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05033","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05033v1","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05033","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"VKLYJQYNPHVT","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"pith_short_16","alias_value":"VKLYJQYNPHVT57ZS","created_at":"2026-07-05T11:33:08Z"},{"alias_kind":"pith_short_8","alias_value":"VKLYJQYN","created_at":"2026-07-05T11:33:08Z"}],"graph_snapshots":[{"event_id":"sha256:76b821c193aa01a6979036546ca3feed7169b2c2d99c50ebd08dda426fdd2b00","target":"graph","created_at":"2026-07-05T11:33:08Z","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/2507.05033/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute Galois groups of number fields into the automorphism group of a regular rooted tree. Our main result is that, for a degree 3 postcritically finite polynomial over a number field, where each finite postcritical point has at least one preimage outside the critical orbits, the associated profinite geometric iterated monodromy group is finitely invariably generated. Moreover, this group is determined by the isomorphism c","authors_text":"Dean Wardell, Mikhail Hlushchanka, Olga Lukina","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-07T14:16:54Z","title":"Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05033","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":"sha256:025267be7b87afa2cb9a6993705aea2eb042fe760c4edf43367b7f1c92477419","target":"record","created_at":"2026-07-05T11:33:08Z","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":"ac223c9a42bd61975c3086a9232411747cb37360c32228bfd35bc034e837500d","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-07T14:16:54Z","title_canon_sha256":"712f201f466381e598d56a935587f6b2be36fa2be84e5b15292d97c26243f6ae"},"schema_version":"1.0","source":{"id":"2507.05033","kind":"arxiv","version":1}},"canonical_sha256":"aa9784c30d79eb3eff3250a7151b85e286c492038c76f841249dfc806b46a238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa9784c30d79eb3eff3250a7151b85e286c492038c76f841249dfc806b46a238","first_computed_at":"2026-07-05T11:33:08.111543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:08.111543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RUTh0xlXKQM/KC0a0iX3Ncxj6S0jVQFQfkYfbGL7lp9UWVeT3X2Sd1EwjjEPXA2+yAqRYM4oOHoWuH+dOuf2Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:08.112018Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.05033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:025267be7b87afa2cb9a6993705aea2eb042fe760c4edf43367b7f1c92477419","sha256:76b821c193aa01a6979036546ca3feed7169b2c2d99c50ebd08dda426fdd2b00"],"state_sha256":"595ae767e6f68c58a8f7e16676a303c1b6fa956a17ec8f459e6f0fefef69242d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Itzq13bDhAAzZoHh6t39sjuKtLDdhlj265VauXL8uz9qDaCgP68qrzBEstdQr8P1zbywPlz6oLJ6JnMbysmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T00:53:39.007554Z","bundle_sha256":"ea4405412097c5dc1338219174c28bd372fa3416eab5e92af65998801a870ca1"}}