{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DNOZARE6W6H6YP3327K7VFKYGB","short_pith_number":"pith:DNOZARE6","canonical_record":{"source":{"id":"1509.05690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-09-11T16:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"e88b77a7c05cb20723501fb441a7c3fcbe84178b119cb8b1cc14c42ccd171ff2","abstract_canon_sha256":"ee82f1ba1d1609587bbda9e6f105b84c1f7135d4181aa0eb5badebb5cfe782a9"},"schema_version":"1.0"},"canonical_sha256":"1b5d90449eb78fec3f7bd7d5fa955830624014227ac5011668be3836ee8c15c2","source":{"kind":"arxiv","id":"1509.05690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05690","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05690v1","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05690","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"pith_short_12","alias_value":"DNOZARE6W6H6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNOZARE6W6H6YP33","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNOZARE6","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DNOZARE6W6H6YP3327K7VFKYGB","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-09-11T16:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"e88b77a7c05cb20723501fb441a7c3fcbe84178b119cb8b1cc14c42ccd171ff2","abstract_canon_sha256":"ee82f1ba1d1609587bbda9e6f105b84c1f7135d4181aa0eb5badebb5cfe782a9"},"schema_version":"1.0"},"canonical_sha256":"1b5d90449eb78fec3f7bd7d5fa955830624014227ac5011668be3836ee8c15c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:42.597127Z","signature_b64":"HmOH7fP+mkFhZyJbcM2UaErfX9Y2ozmtNYDOiLEkcH9GjeSa9DaBVunde3/Ub+a41rTcOohdQuwU3rBOQHLSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b5d90449eb78fec3f7bd7d5fa955830624014227ac5011668be3836ee8c15c2","last_reissued_at":"2026-05-18T01:32:42.596695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:42.596695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05690","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":"2026-05-18T01:32:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rt0N+nfUuseZxnUkxkH8G0QNQ+Bx2tubLdpxkUPiyxiGW5Jp6ilwKCI38icVUxdszMuLeD2u4pbLVLj31zvmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:36:41.466578Z"},"content_sha256":"c56d445290eedc659c6d5b5b37ffa39eb3df79a2bf7a2f01a6bafc50b9eea75b","schema_version":"1.0","event_id":"sha256:c56d445290eedc659c6d5b5b37ffa39eb3df79a2bf7a2f01a6bafc50b9eea75b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DNOZARE6W6H6YP3327K7VFKYGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Yaroslav D. Sergeyev","submitted_at":"2015-09-11T16:54:00Z","abstract_excerpt":"The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA and EU. It is revealed in the paper that at infinity the snowflake is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05690","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":"2026-05-18T01:32:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AY2eO/fP/Kr1P2SWvCbfsV6cFN8TLbLgFFCv6c62hk5sjIPP0+P8ksy+NalVHAwY/F/wIYu/Td35uXsADKNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:36:41.467344Z"},"content_sha256":"f1eae76ef7cb2cd652d5162c3fede5adc06765dd969cabae5c47319d7f660e99","schema_version":"1.0","event_id":"sha256:f1eae76ef7cb2cd652d5162c3fede5adc06765dd969cabae5c47319d7f660e99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNOZARE6W6H6YP3327K7VFKYGB/bundle.json","state_url":"https://pith.science/pith/DNOZARE6W6H6YP3327K7VFKYGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNOZARE6W6H6YP3327K7VFKYGB/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":"2026-05-31T10:36:41Z","links":{"resolver":"https://pith.science/pith/DNOZARE6W6H6YP3327K7VFKYGB","bundle":"https://pith.science/pith/DNOZARE6W6H6YP3327K7VFKYGB/bundle.json","state":"https://pith.science/pith/DNOZARE6W6H6YP3327K7VFKYGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNOZARE6W6H6YP3327K7VFKYGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DNOZARE6W6H6YP3327K7VFKYGB","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":"ee82f1ba1d1609587bbda9e6f105b84c1f7135d4181aa0eb5badebb5cfe782a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-09-11T16:54:00Z","title_canon_sha256":"e88b77a7c05cb20723501fb441a7c3fcbe84178b119cb8b1cc14c42ccd171ff2"},"schema_version":"1.0","source":{"id":"1509.05690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05690","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05690v1","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05690","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"pith_short_12","alias_value":"DNOZARE6W6H6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNOZARE6W6H6YP33","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNOZARE6","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:f1eae76ef7cb2cd652d5162c3fede5adc06765dd969cabae5c47319d7f660e99","target":"graph","created_at":"2026-05-18T01:32:42Z","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 Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA and EU. It is revealed in the paper that at infinity the snowflake is ","authors_text":"Yaroslav D. Sergeyev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-09-11T16:54:00Z","title":"The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05690","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:c56d445290eedc659c6d5b5b37ffa39eb3df79a2bf7a2f01a6bafc50b9eea75b","target":"record","created_at":"2026-05-18T01:32:42Z","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":"ee82f1ba1d1609587bbda9e6f105b84c1f7135d4181aa0eb5badebb5cfe782a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-09-11T16:54:00Z","title_canon_sha256":"e88b77a7c05cb20723501fb441a7c3fcbe84178b119cb8b1cc14c42ccd171ff2"},"schema_version":"1.0","source":{"id":"1509.05690","kind":"arxiv","version":1}},"canonical_sha256":"1b5d90449eb78fec3f7bd7d5fa955830624014227ac5011668be3836ee8c15c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b5d90449eb78fec3f7bd7d5fa955830624014227ac5011668be3836ee8c15c2","first_computed_at":"2026-05-18T01:32:42.596695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:42.596695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HmOH7fP+mkFhZyJbcM2UaErfX9Y2ozmtNYDOiLEkcH9GjeSa9DaBVunde3/Ub+a41rTcOohdQuwU3rBOQHLSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:42.597127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c56d445290eedc659c6d5b5b37ffa39eb3df79a2bf7a2f01a6bafc50b9eea75b","sha256:f1eae76ef7cb2cd652d5162c3fede5adc06765dd969cabae5c47319d7f660e99"],"state_sha256":"1ecb2686eb03f7354b574256dd5bb4724016db3eafe77214f7ef5dd6165670e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cq6CHZLfTvJGazFr8DWBfVKfREa46OGHlQ8hLF211HfynWrtPajkSmnyABoQsoahjr2L7sUnyT/azEGqxSzABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:36:41.471551Z","bundle_sha256":"4db3f9a125b1e1bceb3b4cff59636e7637259d8d69b8e619068404b66248dbb0"}}