{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JRWBPE6JZCFXLLE6AAZ6QWKNJU","short_pith_number":"pith:JRWBPE6J","canonical_record":{"source":{"id":"1310.1258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-02T17:33:25Z","cross_cats_sorted":[],"title_canon_sha256":"dd51703eccc5550e338d565f567f0607abd0f9f70d50e75119f3806b195abd1b","abstract_canon_sha256":"db839fd492bf2437749eb3ed31f9f735472773e938a6c9fee755765c20eeeb30"},"schema_version":"1.0"},"canonical_sha256":"4c6c1793c9c88b75ac9e0033e8594d4d151f22a9189b6eb4c436b0a7a45c16e5","source":{"kind":"arxiv","id":"1310.1258","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1258","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1258v1","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1258","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"JRWBPE6JZCFX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JRWBPE6JZCFXLLE6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JRWBPE6J","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JRWBPE6JZCFXLLE6AAZ6QWKNJU","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-02T17:33:25Z","cross_cats_sorted":[],"title_canon_sha256":"dd51703eccc5550e338d565f567f0607abd0f9f70d50e75119f3806b195abd1b","abstract_canon_sha256":"db839fd492bf2437749eb3ed31f9f735472773e938a6c9fee755765c20eeeb30"},"schema_version":"1.0"},"canonical_sha256":"4c6c1793c9c88b75ac9e0033e8594d4d151f22a9189b6eb4c436b0a7a45c16e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:23.057147Z","signature_b64":"6GYqa535Zk4yhQJUkbjTl77viqPSYdoagexl06/hQQFQXheN6UCMDgXaHxKpogCvQqiz7yC+wZX5CkF1Bnf+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c6c1793c9c88b75ac9e0033e8594d4d151f22a9189b6eb4c436b0a7a45c16e5","last_reissued_at":"2026-05-18T03:11:23.056336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:23.056336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1258","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":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KtI6cqAeGT/k2mp7gvc14FTUq1N5zMRjSft9KinCoA9RIp222nHS1kRSnGBqxO5fpBx/UDt+mOeZAaKmd7HBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:56:59.096269Z"},"content_sha256":"6e5f8a9b1f168ad4a42356960cb2134c3ce64a466a8f78486bbdd111b6fd030f","schema_version":"1.0","event_id":"sha256:6e5f8a9b1f168ad4a42356960cb2134c3ce64a466a8f78486bbdd111b6fd030f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JRWBPE6JZCFXLLE6AAZ6QWKNJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transfinite Asymptotic Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Maciej Satkiewicz","submitted_at":"2013-10-02T17:33:25Z","abstract_excerpt":"Asymptotic property C for metric spaces was introduced by Dranishnikos as generalization of finite asymptotic dimension - asdim. It turns out that this property can be viewed as transfinite extension of asymptotic dimension. The original definition was given by Radul. We introduce three equivalent definitions, show that asymptotic property C is closed under products (open problem stated \"Open problems in topology II\") and prove some other facts, i.e. by defining dimension of a family of metric spaces. Some examples of spaces enjoying countable trasfinite asymptotic dimension are given. We also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1258","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":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhHbhcMlya3d+BbFsj8wJ1L29V59+77NijC5gxmMz8e2Crfkf3HLYYnlKw6BuXcPW9TRcW8MmYEQ2Natv0hmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:56:59.096631Z"},"content_sha256":"6f8b46c67184c56caa86a2defb260376ec1883c2c62cef3898d96643ae9fe47a","schema_version":"1.0","event_id":"sha256:6f8b46c67184c56caa86a2defb260376ec1883c2c62cef3898d96643ae9fe47a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU/bundle.json","state_url":"https://pith.science/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU/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":"2026-05-28T12:56:59Z","links":{"resolver":"https://pith.science/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU","bundle":"https://pith.science/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU/bundle.json","state":"https://pith.science/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JRWBPE6JZCFXLLE6AAZ6QWKNJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JRWBPE6JZCFXLLE6AAZ6QWKNJU","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":"db839fd492bf2437749eb3ed31f9f735472773e938a6c9fee755765c20eeeb30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-02T17:33:25Z","title_canon_sha256":"dd51703eccc5550e338d565f567f0607abd0f9f70d50e75119f3806b195abd1b"},"schema_version":"1.0","source":{"id":"1310.1258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1258","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1258v1","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1258","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"JRWBPE6JZCFX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JRWBPE6JZCFXLLE6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JRWBPE6J","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:6f8b46c67184c56caa86a2defb260376ec1883c2c62cef3898d96643ae9fe47a","target":"graph","created_at":"2026-05-18T03:11:23Z","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":"Asymptotic property C for metric spaces was introduced by Dranishnikos as generalization of finite asymptotic dimension - asdim. It turns out that this property can be viewed as transfinite extension of asymptotic dimension. The original definition was given by Radul. We introduce three equivalent definitions, show that asymptotic property C is closed under products (open problem stated \"Open problems in topology II\") and prove some other facts, i.e. by defining dimension of a family of metric spaces. Some examples of spaces enjoying countable trasfinite asymptotic dimension are given. We also","authors_text":"Maciej Satkiewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-02T17:33:25Z","title":"Transfinite Asymptotic Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1258","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":"sha256:6e5f8a9b1f168ad4a42356960cb2134c3ce64a466a8f78486bbdd111b6fd030f","target":"record","created_at":"2026-05-18T03:11:23Z","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":"db839fd492bf2437749eb3ed31f9f735472773e938a6c9fee755765c20eeeb30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-10-02T17:33:25Z","title_canon_sha256":"dd51703eccc5550e338d565f567f0607abd0f9f70d50e75119f3806b195abd1b"},"schema_version":"1.0","source":{"id":"1310.1258","kind":"arxiv","version":1}},"canonical_sha256":"4c6c1793c9c88b75ac9e0033e8594d4d151f22a9189b6eb4c436b0a7a45c16e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c6c1793c9c88b75ac9e0033e8594d4d151f22a9189b6eb4c436b0a7a45c16e5","first_computed_at":"2026-05-18T03:11:23.056336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:23.056336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6GYqa535Zk4yhQJUkbjTl77viqPSYdoagexl06/hQQFQXheN6UCMDgXaHxKpogCvQqiz7yC+wZX5CkF1Bnf+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:23.057147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e5f8a9b1f168ad4a42356960cb2134c3ce64a466a8f78486bbdd111b6fd030f","sha256:6f8b46c67184c56caa86a2defb260376ec1883c2c62cef3898d96643ae9fe47a"],"state_sha256":"d684fa3106d920d0b53a9caac7122067d4105a39b509608a00c2359cc6978cc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQ39OzNDZuK+QbGXOvmx6dHtb7xr/jCYImj9/wlhwrqa6V6pmICitu3axQgKPG9h5BY4/Gxo6eY4mJgftPKJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:56:59.098559Z","bundle_sha256":"da56bd8b8587a2546ba279b3f25dbc54eb5b64785915c8698437b60255094a7f"}}