{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3IMRK5LDPATNYTSZQVXVY7NGQM","short_pith_number":"pith:3IMRK5LD","canonical_record":{"source":{"id":"1010.2032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-11T08:13:48Z","cross_cats_sorted":[],"title_canon_sha256":"154bd2791df3fe872f2b9b807a022b4adaa3737d8db20ddedcbf481eeb204a13","abstract_canon_sha256":"fe1f515e8b3f6a00ec0cd7fae238b1b113dcd437d7f6ca2533cf1ea117912315"},"schema_version":"1.0"},"canonical_sha256":"da191575637826dc4e59856f5c7da6830deddc514abc8c880dc780d0247ae05b","source":{"kind":"arxiv","id":"1010.2032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2032","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2032v1","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2032","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"3IMRK5LDPATN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3IMRK5LDPATNYTSZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3IMRK5LD","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3IMRK5LDPATNYTSZQVXVY7NGQM","target":"record","payload":{"canonical_record":{"source":{"id":"1010.2032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-11T08:13:48Z","cross_cats_sorted":[],"title_canon_sha256":"154bd2791df3fe872f2b9b807a022b4adaa3737d8db20ddedcbf481eeb204a13","abstract_canon_sha256":"fe1f515e8b3f6a00ec0cd7fae238b1b113dcd437d7f6ca2533cf1ea117912315"},"schema_version":"1.0"},"canonical_sha256":"da191575637826dc4e59856f5c7da6830deddc514abc8c880dc780d0247ae05b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:29.857381Z","signature_b64":"3qqWfNSoqe3wTofx80TlCHSIwEFzhLAWS5//8mNy9L2LFm376svlVIvbK3qArulZIiRMHF7RAGz3EYnZxEZXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da191575637826dc4e59856f5c7da6830deddc514abc8c880dc780d0247ae05b","last_reissued_at":"2026-05-18T04:39:29.856861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:29.856861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.2032","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":"2026-05-18T04:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RAcJmlcYvp43g8mt2oIrM46faXXGzj+ZsG3qxSZz7FXYPd0r3y1iBcCozXaLvsT+pDySJ6GNgi0ytvVQ31PaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:35:48.824806Z"},"content_sha256":"84fc758493babc2aa26b5f1ac32d1e105f0d055a9c64b150a9f180ff1f0c6e77","schema_version":"1.0","event_id":"sha256:84fc758493babc2aa26b5f1ac32d1e105f0d055a9c64b150a9f180ff1f0c6e77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3IMRK5LDPATNYTSZQVXVY7NGQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature Bounds for Neighborhoods of Self-Similar Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Steffen Winter","submitted_at":"2010-10-11T08:13:48Z","abstract_excerpt":"In some recent work, fractal curvatures C^f_k(F) and fractal curvature measures C^f_k(F, .), k = 0, ..., d, have been determined for all self-similar sets F in R^d, for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations of the curvature bound condition and also a very natural techn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2032","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":"2026-05-18T04:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qT6OlDhQaNVyC3MZqhYyAG+xPFvNk3jG6qLAHlu2lDswfoz0KVZeyHztJKgmmW61NisjEmhFuaLZ3VDpNqGLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:35:48.825439Z"},"content_sha256":"d3f82d4174e598960813fb2b522bd17c6e4a56cd8f07a8f44328b5b6bc5ccf6f","schema_version":"1.0","event_id":"sha256:d3f82d4174e598960813fb2b522bd17c6e4a56cd8f07a8f44328b5b6bc5ccf6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IMRK5LDPATNYTSZQVXVY7NGQM/bundle.json","state_url":"https://pith.science/pith/3IMRK5LDPATNYTSZQVXVY7NGQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IMRK5LDPATNYTSZQVXVY7NGQM/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":"2026-06-04T23:35:48Z","links":{"resolver":"https://pith.science/pith/3IMRK5LDPATNYTSZQVXVY7NGQM","bundle":"https://pith.science/pith/3IMRK5LDPATNYTSZQVXVY7NGQM/bundle.json","state":"https://pith.science/pith/3IMRK5LDPATNYTSZQVXVY7NGQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IMRK5LDPATNYTSZQVXVY7NGQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3IMRK5LDPATNYTSZQVXVY7NGQM","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":"fe1f515e8b3f6a00ec0cd7fae238b1b113dcd437d7f6ca2533cf1ea117912315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-11T08:13:48Z","title_canon_sha256":"154bd2791df3fe872f2b9b807a022b4adaa3737d8db20ddedcbf481eeb204a13"},"schema_version":"1.0","source":{"id":"1010.2032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2032","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2032v1","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2032","created_at":"2026-05-18T04:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"3IMRK5LDPATN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3IMRK5LDPATNYTSZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3IMRK5LD","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:d3f82d4174e598960813fb2b522bd17c6e4a56cd8f07a8f44328b5b6bc5ccf6f","target":"graph","created_at":"2026-05-18T04:39:29Z","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 some recent work, fractal curvatures C^f_k(F) and fractal curvature measures C^f_k(F, .), k = 0, ..., d, have been determined for all self-similar sets F in R^d, for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations of the curvature bound condition and also a very natural techn","authors_text":"Steffen Winter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-11T08:13:48Z","title":"Curvature Bounds for Neighborhoods of Self-Similar Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2032","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":"sha256:84fc758493babc2aa26b5f1ac32d1e105f0d055a9c64b150a9f180ff1f0c6e77","target":"record","created_at":"2026-05-18T04:39:29Z","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":"fe1f515e8b3f6a00ec0cd7fae238b1b113dcd437d7f6ca2533cf1ea117912315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-11T08:13:48Z","title_canon_sha256":"154bd2791df3fe872f2b9b807a022b4adaa3737d8db20ddedcbf481eeb204a13"},"schema_version":"1.0","source":{"id":"1010.2032","kind":"arxiv","version":1}},"canonical_sha256":"da191575637826dc4e59856f5c7da6830deddc514abc8c880dc780d0247ae05b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da191575637826dc4e59856f5c7da6830deddc514abc8c880dc780d0247ae05b","first_computed_at":"2026-05-18T04:39:29.856861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:29.856861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3qqWfNSoqe3wTofx80TlCHSIwEFzhLAWS5//8mNy9L2LFm376svlVIvbK3qArulZIiRMHF7RAGz3EYnZxEZXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:29.857381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84fc758493babc2aa26b5f1ac32d1e105f0d055a9c64b150a9f180ff1f0c6e77","sha256:d3f82d4174e598960813fb2b522bd17c6e4a56cd8f07a8f44328b5b6bc5ccf6f"],"state_sha256":"ad563eb04dfd06544769bb506c7e8fa9923d41dc9f0f5ba81aee1d3ed50b867c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMz9GuP+fDWJ8w6ZVfijM7ZgA5v0qE4oCpcdjJ5RT4HQGj9QTP0jqRQ+zAdPL7b1qkRvoFyrAA1/ljt10mWZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:35:48.827598Z","bundle_sha256":"b1587b58b156feeed7b5b1adadc508300a2f42c06f15f91077423289dff9a20f"}}