{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HF2BOD4IG3HRUEKV7R3JFOWCF2","short_pith_number":"pith:HF2BOD4I","canonical_record":{"source":{"id":"1510.02827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-09T21:30:14Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7837c06e01d235f57f435ef4153dc65632a0ec439245d732de98df93ce7ba090","abstract_canon_sha256":"585bca439dc5047bff34d08e7be908ba69ae2bef50604918576cf98e605c1109"},"schema_version":"1.0"},"canonical_sha256":"3974170f8836cf1a1155fc7692bac22ea793e787645b305c8668cda6be1bad50","source":{"kind":"arxiv","id":"1510.02827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02827","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02827v1","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02827","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"HF2BOD4IG3HR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HF2BOD4IG3HRUEKV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HF2BOD4I","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HF2BOD4IG3HRUEKV7R3JFOWCF2","target":"record","payload":{"canonical_record":{"source":{"id":"1510.02827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-09T21:30:14Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7837c06e01d235f57f435ef4153dc65632a0ec439245d732de98df93ce7ba090","abstract_canon_sha256":"585bca439dc5047bff34d08e7be908ba69ae2bef50604918576cf98e605c1109"},"schema_version":"1.0"},"canonical_sha256":"3974170f8836cf1a1155fc7692bac22ea793e787645b305c8668cda6be1bad50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:24.861588Z","signature_b64":"0SLpw9GiIEb0ebVjJe1qs1BleqSlDmmB3xJ5/aPWQVZMFSZ+TShj2aMeCHIuCHZwvsaTVRLESZvreVUW8AKVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3974170f8836cf1a1155fc7692bac22ea793e787645b305c8668cda6be1bad50","last_reissued_at":"2026-05-18T01:10:24.861114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:24.861114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.02827","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":"2026-05-18T01:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hU9sfNHlT8QAZWCXUQT3NmLbLroBX2CRIM3cujC1PCakGWyaL8kFRDVYfLPRPYQSIg/KLfvAm7oa5T+Q7ev/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:07:13.958170Z"},"content_sha256":"c346683209e78124cd0b593a7b37bc7adcc4dde4e3f694f7e6ea2dae08cdd691","schema_version":"1.0","event_id":"sha256:c346683209e78124cd0b593a7b37bc7adcc4dde4e3f694f7e6ea2dae08cdd691"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HF2BOD4IG3HRUEKV7R3JFOWCF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random affine code tree fractals: Hausdorff and affinity dimensions and pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Esa J\\\"arvenp\\\"a\\\"a, Maarit J\\\"arvenp\\\"a\\\"a, Meng Wu, Wen Wu","submitted_at":"2015-10-09T21:30:14Z","abstract_excerpt":"We prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal to the zero of the pressure. In particular, we do not presume the validity of the Falconer-Sloan condition or any other additional assumptions which have been essential in all the previously known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02827","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":"2026-05-18T01:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+RJB88ivvCpCTA6DRaQwhXxofLji0xUsWDcMSIPEo07ycj2rPcGPTSpMzlD62dVqe1FwK8tKQzwCXm7eJkx5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:07:13.958562Z"},"content_sha256":"1c500f2b65f605fd503bbd0d7a761dc4e2670b2debe0ee7df00af33cdc20cfde","schema_version":"1.0","event_id":"sha256:1c500f2b65f605fd503bbd0d7a761dc4e2670b2debe0ee7df00af33cdc20cfde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2/bundle.json","state_url":"https://pith.science/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2/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":"2026-06-05T03:07:13Z","links":{"resolver":"https://pith.science/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2","bundle":"https://pith.science/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2/bundle.json","state":"https://pith.science/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HF2BOD4IG3HRUEKV7R3JFOWCF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HF2BOD4IG3HRUEKV7R3JFOWCF2","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":"585bca439dc5047bff34d08e7be908ba69ae2bef50604918576cf98e605c1109","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-09T21:30:14Z","title_canon_sha256":"7837c06e01d235f57f435ef4153dc65632a0ec439245d732de98df93ce7ba090"},"schema_version":"1.0","source":{"id":"1510.02827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02827","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02827v1","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02827","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"HF2BOD4IG3HR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HF2BOD4IG3HRUEKV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HF2BOD4I","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:1c500f2b65f605fd503bbd0d7a761dc4e2670b2debe0ee7df00af33cdc20cfde","target":"graph","created_at":"2026-05-18T01:10:24Z","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 prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal to the zero of the pressure. In particular, we do not presume the validity of the Falconer-Sloan condition or any other additional assumptions which have been essential in all the previously known results.","authors_text":"Esa J\\\"arvenp\\\"a\\\"a, Maarit J\\\"arvenp\\\"a\\\"a, Meng Wu, Wen Wu","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-09T21:30:14Z","title":"Random affine code tree fractals: Hausdorff and affinity dimensions and pressure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02827","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:c346683209e78124cd0b593a7b37bc7adcc4dde4e3f694f7e6ea2dae08cdd691","target":"record","created_at":"2026-05-18T01:10:24Z","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":"585bca439dc5047bff34d08e7be908ba69ae2bef50604918576cf98e605c1109","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-09T21:30:14Z","title_canon_sha256":"7837c06e01d235f57f435ef4153dc65632a0ec439245d732de98df93ce7ba090"},"schema_version":"1.0","source":{"id":"1510.02827","kind":"arxiv","version":1}},"canonical_sha256":"3974170f8836cf1a1155fc7692bac22ea793e787645b305c8668cda6be1bad50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3974170f8836cf1a1155fc7692bac22ea793e787645b305c8668cda6be1bad50","first_computed_at":"2026-05-18T01:10:24.861114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:24.861114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0SLpw9GiIEb0ebVjJe1qs1BleqSlDmmB3xJ5/aPWQVZMFSZ+TShj2aMeCHIuCHZwvsaTVRLESZvreVUW8AKVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:24.861588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c346683209e78124cd0b593a7b37bc7adcc4dde4e3f694f7e6ea2dae08cdd691","sha256:1c500f2b65f605fd503bbd0d7a761dc4e2670b2debe0ee7df00af33cdc20cfde"],"state_sha256":"f5cef34cf53fef862be073e9ea1b3cb397f2ac7db9ad4092f25190510a2ea3be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z29gWA6mOgxXXJRZRQSI3j7xxuuDDVX2e1k4lFoQnrSGBb4PyCxwk2QwanvS0FUuBUi+T7H8lP+P9LpXpQExAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:07:13.960668Z","bundle_sha256":"47b5fbb7e08910d50058c7f3b78472feb4f8e20e8c871f114fc6b4b380ee3442"}}