{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JS4OLCCB4GXVKHQ7UDYPFFCQE5","short_pith_number":"pith:JS4OLCCB","canonical_record":{"source":{"id":"1304.5987","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-22T15:37:20Z","cross_cats_sorted":["math.GN","math.GT"],"title_canon_sha256":"5012b7491e095c809e4d39b5500d24d1d601d719668ba522ae976b24ae9ee842","abstract_canon_sha256":"ee4549dda3233c75f7fe021a93082147ef723a795c667015712972de9b916236"},"schema_version":"1.0"},"canonical_sha256":"4cb8e58841e1af551e1fa0f0f29450274fca6bf3b8ba16d397411ebef7fd8192","source":{"kind":"arxiv","id":"1304.5987","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5987","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5987v2","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5987","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"JS4OLCCB4GXV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JS4OLCCB4GXVKHQ7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JS4OLCCB","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JS4OLCCB4GXVKHQ7UDYPFFCQE5","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5987","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-22T15:37:20Z","cross_cats_sorted":["math.GN","math.GT"],"title_canon_sha256":"5012b7491e095c809e4d39b5500d24d1d601d719668ba522ae976b24ae9ee842","abstract_canon_sha256":"ee4549dda3233c75f7fe021a93082147ef723a795c667015712972de9b916236"},"schema_version":"1.0"},"canonical_sha256":"4cb8e58841e1af551e1fa0f0f29450274fca6bf3b8ba16d397411ebef7fd8192","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:49.117135Z","signature_b64":"IDoSkV4I+Xckign886rkJvJhOj23DgAQnS8PsTrKibrnk3TMqA3H7cw3CrODo50CVB2PoX/UYlmLi10IiKRdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cb8e58841e1af551e1fa0f0f29450274fca6bf3b8ba16d397411ebef7fd8192","last_reissued_at":"2026-05-18T01:22:49.116451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:49.116451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5987","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avyX5F9KFlRLtbFwjRvUNerTDmw9XyM4R/wAeFmjchp9jO0IUeBMkD38Ty9i1hTZvzeUrsTc8MHU+DNJsUiaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:51:47.742226Z"},"content_sha256":"7e4095621a9f6b0044d4448eb0191427888767f0b26dd783bca63f99ec2e1896","schema_version":"1.0","event_id":"sha256:7e4095621a9f6b0044d4448eb0191427888767f0b26dd783bca63f99ec2e1896"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JS4OLCCB4GXVKHQ7UDYPFFCQE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large scale absolute extensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GT"],"primary_cat":"math.MG","authors_text":"Atish Mitra, Jerzy Dydak","submitted_at":"2013-04-22T15:37:20Z","abstract_excerpt":"This paper is devoted to dualization of dimension-theoretical results from the small scale to the large scale. So far there are two approaches for such dualization: one consisting of creating analogs of small scale concepts and the other amounting to the covering dimension of the Higson corona $\\nu(X)$ of $X$. The first approach was used by M.Gromov when defining the asymptotic dimension $\\asdim(X)$ of metric spaces $X$. The second approach was implicitly contained in the paper \\cite{Dran AsyTop} by Dranishnikov on asymptotic topology. It is not known if the two approaches yield the same conce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5987","kind":"arxiv","version":2},"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":"2026-05-18T01:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWJPuUiUKRNL1iWsL9OgkT81CauCdEfSXnDdx9Qr5Uvf5Cp4IkkN+WQ6LHfrC4fZwRazwOr/PnMZmd1xfTarCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:51:47.742602Z"},"content_sha256":"a1e353b81862f2ec8caf57e7d871cc96c23090e246eb43ea90aed09dfc5e22e1","schema_version":"1.0","event_id":"sha256:a1e353b81862f2ec8caf57e7d871cc96c23090e246eb43ea90aed09dfc5e22e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5/bundle.json","state_url":"https://pith.science/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5/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":"2026-06-23T15:51:47Z","links":{"resolver":"https://pith.science/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5","bundle":"https://pith.science/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5/bundle.json","state":"https://pith.science/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JS4OLCCB4GXVKHQ7UDYPFFCQE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JS4OLCCB4GXVKHQ7UDYPFFCQE5","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":"ee4549dda3233c75f7fe021a93082147ef723a795c667015712972de9b916236","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-22T15:37:20Z","title_canon_sha256":"5012b7491e095c809e4d39b5500d24d1d601d719668ba522ae976b24ae9ee842"},"schema_version":"1.0","source":{"id":"1304.5987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5987","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5987v2","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5987","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"JS4OLCCB4GXV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JS4OLCCB4GXVKHQ7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JS4OLCCB","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:a1e353b81862f2ec8caf57e7d871cc96c23090e246eb43ea90aed09dfc5e22e1","target":"graph","created_at":"2026-05-18T01:22:49Z","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":"This paper is devoted to dualization of dimension-theoretical results from the small scale to the large scale. So far there are two approaches for such dualization: one consisting of creating analogs of small scale concepts and the other amounting to the covering dimension of the Higson corona $\\nu(X)$ of $X$. The first approach was used by M.Gromov when defining the asymptotic dimension $\\asdim(X)$ of metric spaces $X$. The second approach was implicitly contained in the paper \\cite{Dran AsyTop} by Dranishnikov on asymptotic topology. It is not known if the two approaches yield the same conce","authors_text":"Atish Mitra, Jerzy Dydak","cross_cats":["math.GN","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-22T15:37:20Z","title":"Large scale absolute extensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5987","kind":"arxiv","version":2},"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":"sha256:7e4095621a9f6b0044d4448eb0191427888767f0b26dd783bca63f99ec2e1896","target":"record","created_at":"2026-05-18T01:22:49Z","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":"ee4549dda3233c75f7fe021a93082147ef723a795c667015712972de9b916236","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-22T15:37:20Z","title_canon_sha256":"5012b7491e095c809e4d39b5500d24d1d601d719668ba522ae976b24ae9ee842"},"schema_version":"1.0","source":{"id":"1304.5987","kind":"arxiv","version":2}},"canonical_sha256":"4cb8e58841e1af551e1fa0f0f29450274fca6bf3b8ba16d397411ebef7fd8192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cb8e58841e1af551e1fa0f0f29450274fca6bf3b8ba16d397411ebef7fd8192","first_computed_at":"2026-05-18T01:22:49.116451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:49.116451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IDoSkV4I+Xckign886rkJvJhOj23DgAQnS8PsTrKibrnk3TMqA3H7cw3CrODo50CVB2PoX/UYlmLi10IiKRdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:49.117135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e4095621a9f6b0044d4448eb0191427888767f0b26dd783bca63f99ec2e1896","sha256:a1e353b81862f2ec8caf57e7d871cc96c23090e246eb43ea90aed09dfc5e22e1"],"state_sha256":"e1ab12392f7daa8f608bf646f6e08a0c64cdfa17f65546dfb94da3ba7c3c5f27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VrBuFOp+8bkPz+ut9n91zxyi76qFD3+R6Gq8FeH8Nfvu+AEDeCyihHgI2RCmT5xm5M6Q7jjM8+Pnz6JGhSNTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:51:47.744568Z","bundle_sha256":"04b0e6dab01cd92ba78ae7b58470cd7cf8bed9cba0dd7c14c61eed14a23451e7"}}