{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:TJUH4V2OABWY6OGLSLNSSH4GUZ","short_pith_number":"pith:TJUH4V2O","canonical_record":{"source":{"id":"0705.0135","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-05-01T16:30:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"346e8f35d01a553b578efae06d5637ee29096ed9b2b7d60c7dfbe3ad9a8c4e55","abstract_canon_sha256":"d9db08d1ca23f15f9c7af4775d39ec3dbbe966bebbbdf596afe3a0939736fe04"},"schema_version":"1.0"},"canonical_sha256":"9a687e574e006d8f38cb92db291f86a675a9915d4cdba898e9f671447147066e","source":{"kind":"arxiv","id":"0705.0135","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.0135","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"0705.0135v1","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.0135","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"TJUH4V2OABWY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TJUH4V2OABWY6OGL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TJUH4V2O","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:TJUH4V2OABWY6OGLSLNSSH4GUZ","target":"record","payload":{"canonical_record":{"source":{"id":"0705.0135","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-05-01T16:30:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"346e8f35d01a553b578efae06d5637ee29096ed9b2b7d60c7dfbe3ad9a8c4e55","abstract_canon_sha256":"d9db08d1ca23f15f9c7af4775d39ec3dbbe966bebbbdf596afe3a0939736fe04"},"schema_version":"1.0"},"canonical_sha256":"9a687e574e006d8f38cb92db291f86a675a9915d4cdba898e9f671447147066e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:32.079812Z","signature_b64":"pC8aQ+PaC3XuA1qLBanQLULviE42pEHZf8Wp7qylj1rECG4X4Zq0RRNx4qrBqo7GtCjSo3ZSkO5HOTciIfNKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a687e574e006d8f38cb92db291f86a675a9915d4cdba898e9f671447147066e","last_reissued_at":"2026-05-17T23:47:32.079189Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:32.079189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.0135","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":"2026-05-17T23:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnzk9Uas/xwxsESbnZsV2K9bFdZ4A/LWIiZb27UqDoozGmTko92jl3oV2xAdh1zf01EuulQkp+I/77/9ijzLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:09:26.855814Z"},"content_sha256":"48a1543ee8660bbbd143183959b5e188c093a847b0ae75c57f7ed0a0a7b18656","schema_version":"1.0","event_id":"sha256:48a1543ee8660bbbd143183959b5e188c093a847b0ae75c57f7ed0a0a7b18656"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:TJUH4V2OABWY6OGLSLNSSH4GUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Packing-Dimension Profiles and Fractional Brownian Motion","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Yimin Xiao","submitted_at":"2007-05-01T16:30:48Z","abstract_excerpt":"In order to compute the packing dimension of orthogonal projections\n  Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently, Howroyd (2001) introduced alternate $s$-dimensional packing dimension profiles $\\hbox{${\\rm P}$-$\\dim$}_s$ and proved, among many other things, that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all integers $s>0$ and all analytic sets $E\\subseteq\\R^N$. The goal of this article is to prove that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all real numbers $s>0$ and analyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0135","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":"2026-05-17T23:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVRvIFShTnkpobaQ/YYReWR9u/4sHmBldqrPZQr1I6ISxH13zHOfY8uwsomxGRVWMUHJuZYjzX5L5QCi4CbqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:09:26.856541Z"},"content_sha256":"74f99901c452e8bb2dd07f15fe2d9ceb1fbf2baff09e45a9d1f26ff642f78d25","schema_version":"1.0","event_id":"sha256:74f99901c452e8bb2dd07f15fe2d9ceb1fbf2baff09e45a9d1f26ff642f78d25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ/bundle.json","state_url":"https://pith.science/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ/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":"2026-06-05T07:09:26Z","links":{"resolver":"https://pith.science/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ","bundle":"https://pith.science/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ/bundle.json","state":"https://pith.science/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJUH4V2OABWY6OGLSLNSSH4GUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TJUH4V2OABWY6OGLSLNSSH4GUZ","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":"d9db08d1ca23f15f9c7af4775d39ec3dbbe966bebbbdf596afe3a0939736fe04","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.PR","submitted_at":"2007-05-01T16:30:48Z","title_canon_sha256":"346e8f35d01a553b578efae06d5637ee29096ed9b2b7d60c7dfbe3ad9a8c4e55"},"schema_version":"1.0","source":{"id":"0705.0135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.0135","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"0705.0135v1","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.0135","created_at":"2026-05-17T23:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"TJUH4V2OABWY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TJUH4V2OABWY6OGL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TJUH4V2O","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:74f99901c452e8bb2dd07f15fe2d9ceb1fbf2baff09e45a9d1f26ff642f78d25","target":"graph","created_at":"2026-05-17T23:47:32Z","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 order to compute the packing dimension of orthogonal projections\n  Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently, Howroyd (2001) introduced alternate $s$-dimensional packing dimension profiles $\\hbox{${\\rm P}$-$\\dim$}_s$ and proved, among many other things, that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all integers $s>0$ and all analytic sets $E\\subseteq\\R^N$. The goal of this article is to prove that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all real numbers $s>0$ and analyt","authors_text":"Davar Khoshnevisan, Yimin Xiao","cross_cats":["math.CA"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-05-01T16:30:48Z","title":"Packing-Dimension Profiles and Fractional Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0135","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":"sha256:48a1543ee8660bbbd143183959b5e188c093a847b0ae75c57f7ed0a0a7b18656","target":"record","created_at":"2026-05-17T23:47:32Z","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":"d9db08d1ca23f15f9c7af4775d39ec3dbbe966bebbbdf596afe3a0939736fe04","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.PR","submitted_at":"2007-05-01T16:30:48Z","title_canon_sha256":"346e8f35d01a553b578efae06d5637ee29096ed9b2b7d60c7dfbe3ad9a8c4e55"},"schema_version":"1.0","source":{"id":"0705.0135","kind":"arxiv","version":1}},"canonical_sha256":"9a687e574e006d8f38cb92db291f86a675a9915d4cdba898e9f671447147066e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a687e574e006d8f38cb92db291f86a675a9915d4cdba898e9f671447147066e","first_computed_at":"2026-05-17T23:47:32.079189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:32.079189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pC8aQ+PaC3XuA1qLBanQLULviE42pEHZf8Wp7qylj1rECG4X4Zq0RRNx4qrBqo7GtCjSo3ZSkO5HOTciIfNKDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:32.079812Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.0135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48a1543ee8660bbbd143183959b5e188c093a847b0ae75c57f7ed0a0a7b18656","sha256:74f99901c452e8bb2dd07f15fe2d9ceb1fbf2baff09e45a9d1f26ff642f78d25"],"state_sha256":"b7370d13bf4a63ca2003d345d1952475e420da32ad63172289b26ab788831286"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVT7h55FGwAAP98AZQnbS2DnkmsO84Stw+rV+UEq8XOIjluxJ4BvJKMB3EfW2qouKlfBAnc3KWKVpfvugNOGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:09:26.860124Z","bundle_sha256":"7a87065a3de7e73408687a8336fd424394a18e7d37f6c45cfa1cb3b9618f56f4"}}