{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:DSZOTAU7YZS3AU6E26XAI6DHNO","short_pith_number":"pith:DSZOTAU7","canonical_record":{"source":{"id":"math/0611177","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2006-11-07T10:26:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f91b92f98b40ec349a034229dd2b96facc11b70ada253f3cc4b08ee69d82719d","abstract_canon_sha256":"6ede60e10bc048a084bfe2ae6fa2dd11bd31be3531d1fbdc52b218891f74fffd"},"schema_version":"1.0"},"canonical_sha256":"1cb2e9829fc665b053c4d7ae0478676b974dae5dbce5c546a7a036049f524a2e","source":{"kind":"arxiv","id":"math/0611177","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611177","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611177v2","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611177","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"DSZOTAU7YZS3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DSZOTAU7YZS3AU6E","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DSZOTAU7","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:DSZOTAU7YZS3AU6E26XAI6DHNO","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611177","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2006-11-07T10:26:09Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f91b92f98b40ec349a034229dd2b96facc11b70ada253f3cc4b08ee69d82719d","abstract_canon_sha256":"6ede60e10bc048a084bfe2ae6fa2dd11bd31be3531d1fbdc52b218891f74fffd"},"schema_version":"1.0"},"canonical_sha256":"1cb2e9829fc665b053c4d7ae0478676b974dae5dbce5c546a7a036049f524a2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.170639Z","signature_b64":"kcFcBWGiYulZFT/d9pBFDlBmDGOA0zBqwOSTQAMgTnzV1lXj80CaxJ0FKsvhXtwoN+YlTRLwcHM1lrf6XRTlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb2e9829fc665b053c4d7ae0478676b974dae5dbce5c546a7a036049f524a2e","last_reissued_at":"2026-05-18T01:11:52.170296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.170296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611177","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXwsH3WGFEwBZglcCniB1SctlzY8EATbK2zhWFImeJDuF28edzUG9XBxOz4F0m3gFlN1Tr1hNtVidGdKIoTeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:45:02.813813Z"},"content_sha256":"9456c3eb322d194663d39c7722877c12811633c7d76ae8f18e003ba98ace7b83","schema_version":"1.0","event_id":"sha256:9456c3eb322d194663d39c7722877c12811633c7d76ae8f18e003ba98ace7b83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:DSZOTAU7YZS3AU6E26XAI6DHNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterated Monodromy Groups of Quadratic Polynomials, I","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Laurent Bartholdi, Volodymyr V. Nekrashevych","submitted_at":"2006-11-07T10:26:09Z","abstract_excerpt":"We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the `kneading sequence' of the polynomial.\n  We then give recursive presentations by generators and relations for these groups, and study some of their properties, like torsion and `branchness'."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611177","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7x6lt++NTNs+Zh9bVYHtz3ckho0vkXRM/FmZOFw03JFrf+u5KW6af5bRHI9UPXBXypl36Jbphp9O23QFBXOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:45:02.814591Z"},"content_sha256":"dd241e5230f6aaa70a72ad1655dfa3da0b10a9d10073187baaa780ae6656eb7c","schema_version":"1.0","event_id":"sha256:dd241e5230f6aaa70a72ad1655dfa3da0b10a9d10073187baaa780ae6656eb7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSZOTAU7YZS3AU6E26XAI6DHNO/bundle.json","state_url":"https://pith.science/pith/DSZOTAU7YZS3AU6E26XAI6DHNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSZOTAU7YZS3AU6E26XAI6DHNO/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":"2026-06-10T10:45:02Z","links":{"resolver":"https://pith.science/pith/DSZOTAU7YZS3AU6E26XAI6DHNO","bundle":"https://pith.science/pith/DSZOTAU7YZS3AU6E26XAI6DHNO/bundle.json","state":"https://pith.science/pith/DSZOTAU7YZS3AU6E26XAI6DHNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSZOTAU7YZS3AU6E26XAI6DHNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DSZOTAU7YZS3AU6E26XAI6DHNO","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":"6ede60e10bc048a084bfe2ae6fa2dd11bd31be3531d1fbdc52b218891f74fffd","cross_cats_sorted":["math.DS"],"license":"","primary_cat":"math.GR","submitted_at":"2006-11-07T10:26:09Z","title_canon_sha256":"f91b92f98b40ec349a034229dd2b96facc11b70ada253f3cc4b08ee69d82719d"},"schema_version":"1.0","source":{"id":"math/0611177","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611177","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611177v2","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611177","created_at":"2026-05-18T01:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"DSZOTAU7YZS3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DSZOTAU7YZS3AU6E","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DSZOTAU7","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:dd241e5230f6aaa70a72ad1655dfa3da0b10a9d10073187baaa780ae6656eb7c","target":"graph","created_at":"2026-05-18T01:11:52Z","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"},"paper":{"abstract_excerpt":"We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the `kneading sequence' of the polynomial.\n  We then give recursive presentations by generators and relations for these groups, and study some of their properties, like torsion and `branchness'.","authors_text":"Laurent Bartholdi, Volodymyr V. Nekrashevych","cross_cats":["math.DS"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2006-11-07T10:26:09Z","title":"Iterated Monodromy Groups of Quadratic Polynomials, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611177","kind":"arxiv","version":2},"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":"sha256:9456c3eb322d194663d39c7722877c12811633c7d76ae8f18e003ba98ace7b83","target":"record","created_at":"2026-05-18T01:11:52Z","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":"6ede60e10bc048a084bfe2ae6fa2dd11bd31be3531d1fbdc52b218891f74fffd","cross_cats_sorted":["math.DS"],"license":"","primary_cat":"math.GR","submitted_at":"2006-11-07T10:26:09Z","title_canon_sha256":"f91b92f98b40ec349a034229dd2b96facc11b70ada253f3cc4b08ee69d82719d"},"schema_version":"1.0","source":{"id":"math/0611177","kind":"arxiv","version":2}},"canonical_sha256":"1cb2e9829fc665b053c4d7ae0478676b974dae5dbce5c546a7a036049f524a2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cb2e9829fc665b053c4d7ae0478676b974dae5dbce5c546a7a036049f524a2e","first_computed_at":"2026-05-18T01:11:52.170296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:52.170296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kcFcBWGiYulZFT/d9pBFDlBmDGOA0zBqwOSTQAMgTnzV1lXj80CaxJ0FKsvhXtwoN+YlTRLwcHM1lrf6XRTlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:52.170639Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611177","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9456c3eb322d194663d39c7722877c12811633c7d76ae8f18e003ba98ace7b83","sha256:dd241e5230f6aaa70a72ad1655dfa3da0b10a9d10073187baaa780ae6656eb7c"],"state_sha256":"2625f7bf0b70c823117c2f5ffbc543f5d812cbe16d3c1338ccf2f82f727be276"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTVCtfbQbv8y8wl80xlx4Z5L5irfDZXVu9iH4PUtkNuKtMAvmJf2WYvGuhvkGzXfMJWB6mIKP6AdaxhwIk+9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:45:02.818949Z","bundle_sha256":"19faf32c6c795e7f558ef8c921082030063cd1a9e310557c1d659d0b0249013f"}}