{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:H2P66POZ4TMGJA4KC7663SPUAY","short_pith_number":"pith:H2P66POZ","canonical_record":{"source":{"id":"1203.2724","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T07:04:13Z","cross_cats_sorted":[],"title_canon_sha256":"144cdbe42755d311bc2551769d43d18959f2770958473a0e95795ca1e8db8e5b","abstract_canon_sha256":"1c42d857e6c976c3e27ebc3712d9c286986361bdcbcdd69356f4ad83f8858f03"},"schema_version":"1.0"},"canonical_sha256":"3e9fef3dd9e4d864838a17fdedc9f40617af64fe13cfdd1c6cd06c44de3fec73","source":{"kind":"arxiv","id":"1203.2724","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2724","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2724v5","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2724","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"H2P66POZ4TMG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H2P66POZ4TMGJA4K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H2P66POZ","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:H2P66POZ4TMGJA4KC7663SPUAY","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2724","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T07:04:13Z","cross_cats_sorted":[],"title_canon_sha256":"144cdbe42755d311bc2551769d43d18959f2770958473a0e95795ca1e8db8e5b","abstract_canon_sha256":"1c42d857e6c976c3e27ebc3712d9c286986361bdcbcdd69356f4ad83f8858f03"},"schema_version":"1.0"},"canonical_sha256":"3e9fef3dd9e4d864838a17fdedc9f40617af64fe13cfdd1c6cd06c44de3fec73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:49.597705Z","signature_b64":"HlVp3N01nIP02YGMkbk8Y8kpvwQa5rRX8cDcMjJEza6swe5VU97qVt8ePFuAaeMrnYGRxX/bYHY7lzKK46v3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e9fef3dd9e4d864838a17fdedc9f40617af64fe13cfdd1c6cd06c44de3fec73","last_reissued_at":"2026-05-17T23:50:49.597069Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:49.597069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2724","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5WRT7WpdtXpIPhktdk6mtDyJxPFyp39ohjdI8seSdboos6Y/k3wQXrT+/WDtX9asODkJ+TTiCoKK2QUKiLwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T05:46:02.380660Z"},"content_sha256":"8cadd0f53e1afd97e74fb75554e53fbb058d786ccaa5672555991cb9d3eda02e","schema_version":"1.0","event_id":"sha256:8cadd0f53e1afd97e74fb75554e53fbb058d786ccaa5672555991cb9d3eda02e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:H2P66POZ4TMGJA4KC7663SPUAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological pressure and fractal dimensions of cookie-cutter-like sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mrinal Kanti Roychowdhury","submitted_at":"2012-03-13T07:04:13Z","abstract_excerpt":"The cookie-cutter-like set is defined as the limit set of a sequence of classical cookie-cutter mappings. For this cookie-cutter set it is shown that the topological pressure function exists, and that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension are all equal to the unique zero $h$ of the pressure function. Moreover, it is shown that the $h$-dimensional Hausdorff measure and the $h$-dimensional packing measure are finite and positive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2724","kind":"arxiv","version":5},"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":"2026-05-17T23:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJjqk3I8nh/ceAdqBAmyEwr+NkmwhsnRZYO0D4HzYxSDuw3oPmZHp2IbqmjaMJg+aGaw7GsI3M6+Hd0KdA84Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T05:46:02.381009Z"},"content_sha256":"2f956638dd4204269b0a866cc29844406b7d2a6829371a4c2ee24105a827b1fe","schema_version":"1.0","event_id":"sha256:2f956638dd4204269b0a866cc29844406b7d2a6829371a4c2ee24105a827b1fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2P66POZ4TMGJA4KC7663SPUAY/bundle.json","state_url":"https://pith.science/pith/H2P66POZ4TMGJA4KC7663SPUAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2P66POZ4TMGJA4KC7663SPUAY/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":"2026-06-22T05:46:02Z","links":{"resolver":"https://pith.science/pith/H2P66POZ4TMGJA4KC7663SPUAY","bundle":"https://pith.science/pith/H2P66POZ4TMGJA4KC7663SPUAY/bundle.json","state":"https://pith.science/pith/H2P66POZ4TMGJA4KC7663SPUAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2P66POZ4TMGJA4KC7663SPUAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H2P66POZ4TMGJA4KC7663SPUAY","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":"1c42d857e6c976c3e27ebc3712d9c286986361bdcbcdd69356f4ad83f8858f03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T07:04:13Z","title_canon_sha256":"144cdbe42755d311bc2551769d43d18959f2770958473a0e95795ca1e8db8e5b"},"schema_version":"1.0","source":{"id":"1203.2724","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2724","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2724v5","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2724","created_at":"2026-05-17T23:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"H2P66POZ4TMG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H2P66POZ4TMGJA4K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H2P66POZ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:2f956638dd4204269b0a866cc29844406b7d2a6829371a4c2ee24105a827b1fe","target":"graph","created_at":"2026-05-17T23:50:49Z","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":"The cookie-cutter-like set is defined as the limit set of a sequence of classical cookie-cutter mappings. For this cookie-cutter set it is shown that the topological pressure function exists, and that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension are all equal to the unique zero $h$ of the pressure function. Moreover, it is shown that the $h$-dimensional Hausdorff measure and the $h$-dimensional packing measure are finite and positive.","authors_text":"Mrinal Kanti Roychowdhury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T07:04:13Z","title":"Topological pressure and fractal dimensions of cookie-cutter-like sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2724","kind":"arxiv","version":5},"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":"sha256:8cadd0f53e1afd97e74fb75554e53fbb058d786ccaa5672555991cb9d3eda02e","target":"record","created_at":"2026-05-17T23:50:49Z","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":"1c42d857e6c976c3e27ebc3712d9c286986361bdcbcdd69356f4ad83f8858f03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-13T07:04:13Z","title_canon_sha256":"144cdbe42755d311bc2551769d43d18959f2770958473a0e95795ca1e8db8e5b"},"schema_version":"1.0","source":{"id":"1203.2724","kind":"arxiv","version":5}},"canonical_sha256":"3e9fef3dd9e4d864838a17fdedc9f40617af64fe13cfdd1c6cd06c44de3fec73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e9fef3dd9e4d864838a17fdedc9f40617af64fe13cfdd1c6cd06c44de3fec73","first_computed_at":"2026-05-17T23:50:49.597069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:49.597069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlVp3N01nIP02YGMkbk8Y8kpvwQa5rRX8cDcMjJEza6swe5VU97qVt8ePFuAaeMrnYGRxX/bYHY7lzKK46v3AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:49.597705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2724","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cadd0f53e1afd97e74fb75554e53fbb058d786ccaa5672555991cb9d3eda02e","sha256:2f956638dd4204269b0a866cc29844406b7d2a6829371a4c2ee24105a827b1fe"],"state_sha256":"395c79230c7b1a318fe179595c4ff785a6db3c555f3b69e78ac52e40a7b43eef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4RJssBxNi/IKoNHv+xVLr62QaBLinlMR1l+UNPh6ztDmNeJGEp/HBPfQ5r6Yc3n2s+jaS+RzbKeATJ0NxJoZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T05:46:02.382904Z","bundle_sha256":"c0992a74278ea910265f0da51ce35577abb33c40c4dc4a5f0b5d61c542c3785c"}}