{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3DZHWSNGVHPNWKGM4JW3WND7M3","short_pith_number":"pith:3DZHWSNG","canonical_record":{"source":{"id":"1210.8285","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2012-10-31T10:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"f4a6436223dd0e9862b092ccd909917123e7fa91ae68706cf544aa321cd645f8","abstract_canon_sha256":"65e9c1d5b91caf99b2d15b0cacccaa47f0851004ec68ea07228f7dae6513ecf8"},"schema_version":"1.0"},"canonical_sha256":"d8f27b49a6a9dedb28cce26dbb347f66e08cc77e629707c3e33b0017050d1447","source":{"kind":"arxiv","id":"1210.8285","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.8285","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.8285v1","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8285","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"pith_short_12","alias_value":"3DZHWSNGVHPN","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3DZHWSNGVHPNWKGM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3DZHWSNG","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3DZHWSNGVHPNWKGM4JW3WND7M3","target":"record","payload":{"canonical_record":{"source":{"id":"1210.8285","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2012-10-31T10:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"f4a6436223dd0e9862b092ccd909917123e7fa91ae68706cf544aa321cd645f8","abstract_canon_sha256":"65e9c1d5b91caf99b2d15b0cacccaa47f0851004ec68ea07228f7dae6513ecf8"},"schema_version":"1.0"},"canonical_sha256":"d8f27b49a6a9dedb28cce26dbb347f66e08cc77e629707c3e33b0017050d1447","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:55.440197Z","signature_b64":"saGOHEhM0rZyz7n41/LUa3mKqwozxb/otl9FOFzT2F0t3NkBEkurnaO9AB7H0NaREvID0ooME0soThDdZZPODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8f27b49a6a9dedb28cce26dbb347f66e08cc77e629707c3e33b0017050d1447","last_reissued_at":"2026-05-18T03:41:55.439311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:55.439311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.8285","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":"2026-05-18T03:41:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZo3zu5Pm07tnTGs8W5G7HitR9EcpIk6HWZycI6f1qzCcG5QDLBzxuAa2CSs7Y37ZIKmAxuwGrVWxVYvQq0ZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:37:30.201704Z"},"content_sha256":"2d947ccdc86c8fb72fcedb1b98346e41a23217ca68994e33f17a75487dec12c5","schema_version":"1.0","event_id":"sha256:2d947ccdc86c8fb72fcedb1b98346e41a23217ca68994e33f17a75487dec12c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3DZHWSNGVHPNWKGM4JW3WND7M3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Poincare series of unicritical polynomials at the critical point","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Juan Rivera-Letelier, Weixiao Shen","submitted_at":"2012-10-31T10:20:23Z","abstract_excerpt":"In this paper, we show that for a unicritical polynomial having a priori bounds, the unique conformal measure of minimal exponent has no atom at the critical point. For a conformal measure of higher exponent, we give a necessary and sufficient condition for the critical point to be an atom, in terms of the growth rate of the derivatives at the critical value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8285","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":""},"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":"2026-05-18T03:41:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+aHCiDKrYqaziym30WMoqvGCL+IcLF7x4WavCBlQGiwtQZuzrv5myYjoIzeaZSLHRMDWTWd4GvcxSF3l661BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:37:30.202048Z"},"content_sha256":"83001519cd8a9aa052e567daea3abfbf0c03add3f204654ae7d99bd0dd352a23","schema_version":"1.0","event_id":"sha256:83001519cd8a9aa052e567daea3abfbf0c03add3f204654ae7d99bd0dd352a23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DZHWSNGVHPNWKGM4JW3WND7M3/bundle.json","state_url":"https://pith.science/pith/3DZHWSNGVHPNWKGM4JW3WND7M3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DZHWSNGVHPNWKGM4JW3WND7M3/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":"2026-06-22T14:37:30Z","links":{"resolver":"https://pith.science/pith/3DZHWSNGVHPNWKGM4JW3WND7M3","bundle":"https://pith.science/pith/3DZHWSNGVHPNWKGM4JW3WND7M3/bundle.json","state":"https://pith.science/pith/3DZHWSNGVHPNWKGM4JW3WND7M3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DZHWSNGVHPNWKGM4JW3WND7M3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3DZHWSNGVHPNWKGM4JW3WND7M3","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":"65e9c1d5b91caf99b2d15b0cacccaa47f0851004ec68ea07228f7dae6513ecf8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2012-10-31T10:20:23Z","title_canon_sha256":"f4a6436223dd0e9862b092ccd909917123e7fa91ae68706cf544aa321cd645f8"},"schema_version":"1.0","source":{"id":"1210.8285","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.8285","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.8285v1","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8285","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"pith_short_12","alias_value":"3DZHWSNGVHPN","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3DZHWSNGVHPNWKGM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3DZHWSNG","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:83001519cd8a9aa052e567daea3abfbf0c03add3f204654ae7d99bd0dd352a23","target":"graph","created_at":"2026-05-18T03:41:55Z","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":"In this paper, we show that for a unicritical polynomial having a priori bounds, the unique conformal measure of minimal exponent has no atom at the critical point. For a conformal measure of higher exponent, we give a necessary and sufficient condition for the critical point to be an atom, in terms of the growth rate of the derivatives at the critical value.","authors_text":"Juan Rivera-Letelier, Weixiao Shen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2012-10-31T10:20:23Z","title":"On Poincare series of unicritical polynomials at the critical point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8285","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":"sha256:2d947ccdc86c8fb72fcedb1b98346e41a23217ca68994e33f17a75487dec12c5","target":"record","created_at":"2026-05-18T03:41:55Z","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":"65e9c1d5b91caf99b2d15b0cacccaa47f0851004ec68ea07228f7dae6513ecf8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2012-10-31T10:20:23Z","title_canon_sha256":"f4a6436223dd0e9862b092ccd909917123e7fa91ae68706cf544aa321cd645f8"},"schema_version":"1.0","source":{"id":"1210.8285","kind":"arxiv","version":1}},"canonical_sha256":"d8f27b49a6a9dedb28cce26dbb347f66e08cc77e629707c3e33b0017050d1447","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8f27b49a6a9dedb28cce26dbb347f66e08cc77e629707c3e33b0017050d1447","first_computed_at":"2026-05-18T03:41:55.439311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:55.439311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"saGOHEhM0rZyz7n41/LUa3mKqwozxb/otl9FOFzT2F0t3NkBEkurnaO9AB7H0NaREvID0ooME0soThDdZZPODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:55.440197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.8285","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d947ccdc86c8fb72fcedb1b98346e41a23217ca68994e33f17a75487dec12c5","sha256:83001519cd8a9aa052e567daea3abfbf0c03add3f204654ae7d99bd0dd352a23"],"state_sha256":"09568af77ee794911d41facc06bd3a8f4b8a74f5f67746a7c46a93abf597b1b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7WGIo7TaQg/OWcjEVnynaKkElhL6QU2RSwtjQOQXieoZWUbkjBE9bZhIf+hd8fAeA06HPpKHIjU4Qy9jiFvnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:37:30.204030Z","bundle_sha256":"cbe2893e322511fccd9041a6195c4d5b288b9db71c576ba86baa2e7dcc763f1d"}}