{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q7UNZKCUQRQS4YM3Y2E2COTCAB","short_pith_number":"pith:Q7UNZKCU","canonical_record":{"source":{"id":"1305.7495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-31T17:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"156cd678dbbe3af6e364a4b10e2af94e16b60b250b016aec4b86bdf45db9a0d2","abstract_canon_sha256":"2177b45a5395a831665b5df85661941f132597b4797cfd0981a2fe996e03dbe5"},"schema_version":"1.0"},"canonical_sha256":"87e8dca85484612e619bc689a13a62005befde8da0093505496d8756893e8ac9","source":{"kind":"arxiv","id":"1305.7495","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7495","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7495v3","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7495","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"Q7UNZKCUQRQS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q7UNZKCUQRQS4YM3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q7UNZKCU","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q7UNZKCUQRQS4YM3Y2E2COTCAB","target":"record","payload":{"canonical_record":{"source":{"id":"1305.7495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-31T17:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"156cd678dbbe3af6e364a4b10e2af94e16b60b250b016aec4b86bdf45db9a0d2","abstract_canon_sha256":"2177b45a5395a831665b5df85661941f132597b4797cfd0981a2fe996e03dbe5"},"schema_version":"1.0"},"canonical_sha256":"87e8dca85484612e619bc689a13a62005befde8da0093505496d8756893e8ac9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:42.980001Z","signature_b64":"JnEVLfq/kUyohkk386w5/9xfk1HF/wuSh8/3f48NuaR5Oj5TAcYVMjHqQa9+d/UKc/YtSHRTiVqT9rzPVBj9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87e8dca85484612e619bc689a13a62005befde8da0093505496d8756893e8ac9","last_reissued_at":"2026-05-18T03:21:42.979367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:42.979367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.7495","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hMWv3Pfo2cy1PGmcqomy4GEReZD3Y3PrCHd+u2HeviSZ57QEEZE8KGI4jAWRRI8fGQPYHCELvrDP6WfohpgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:55:57.851074Z"},"content_sha256":"a5e53938af719b9154068b5528ac7f31b8a796fe4edf74204e24fc6d5d4a94b9","schema_version":"1.0","event_id":"sha256:a5e53938af719b9154068b5528ac7f31b8a796fe4edf74204e24fc6d5d4a94b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q7UNZKCUQRQS4YM3Y2E2COTCAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Structure of Dimension Functions of Certain Continuous Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Francesc Perera, Henning Petzka, Joan Bosa, Ramon Antoine","submitted_at":"2013-05-31T17:57:44Z","abstract_excerpt":"In this paper we study structural properties of the Cuntz semigroup and its functionals for continuous fields of C*-algebras over finite dimensional spaces. In a variety of cases, this leads to an answer to a conjecture posed by Blackadar and Handelman. Enroute to our results, we determine when the stable rank of continuous fields of C*-algebras over one dimensional spaces is one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7495","kind":"arxiv","version":3},"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":"2026-05-18T03:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xiXFuuHUHfL4GTSqBdCtqxH+DYzgXtEUBwYCpKj4ZtdIGaURky7ZxOd1u/YOVqJgm4a2YYK4nnc+fV718a78Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:55:57.851421Z"},"content_sha256":"3505b4eebb1fb85a98e68e8f40797c31c4210de8fa192269b2a7d6f303322776","schema_version":"1.0","event_id":"sha256:3505b4eebb1fb85a98e68e8f40797c31c4210de8fa192269b2a7d6f303322776"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB/bundle.json","state_url":"https://pith.science/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB/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":"2026-06-23T03:55:57Z","links":{"resolver":"https://pith.science/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB","bundle":"https://pith.science/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB/bundle.json","state":"https://pith.science/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7UNZKCUQRQS4YM3Y2E2COTCAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q7UNZKCUQRQS4YM3Y2E2COTCAB","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":"2177b45a5395a831665b5df85661941f132597b4797cfd0981a2fe996e03dbe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-31T17:57:44Z","title_canon_sha256":"156cd678dbbe3af6e364a4b10e2af94e16b60b250b016aec4b86bdf45db9a0d2"},"schema_version":"1.0","source":{"id":"1305.7495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7495","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7495v3","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7495","created_at":"2026-05-18T03:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"Q7UNZKCUQRQS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q7UNZKCUQRQS4YM3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q7UNZKCU","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:3505b4eebb1fb85a98e68e8f40797c31c4210de8fa192269b2a7d6f303322776","target":"graph","created_at":"2026-05-18T03:21:42Z","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":"In this paper we study structural properties of the Cuntz semigroup and its functionals for continuous fields of C*-algebras over finite dimensional spaces. In a variety of cases, this leads to an answer to a conjecture posed by Blackadar and Handelman. Enroute to our results, we determine when the stable rank of continuous fields of C*-algebras over one dimensional spaces is one.","authors_text":"Francesc Perera, Henning Petzka, Joan Bosa, Ramon Antoine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-31T17:57:44Z","title":"Geometric Structure of Dimension Functions of Certain Continuous Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7495","kind":"arxiv","version":3},"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:a5e53938af719b9154068b5528ac7f31b8a796fe4edf74204e24fc6d5d4a94b9","target":"record","created_at":"2026-05-18T03:21:42Z","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":"2177b45a5395a831665b5df85661941f132597b4797cfd0981a2fe996e03dbe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-31T17:57:44Z","title_canon_sha256":"156cd678dbbe3af6e364a4b10e2af94e16b60b250b016aec4b86bdf45db9a0d2"},"schema_version":"1.0","source":{"id":"1305.7495","kind":"arxiv","version":3}},"canonical_sha256":"87e8dca85484612e619bc689a13a62005befde8da0093505496d8756893e8ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87e8dca85484612e619bc689a13a62005befde8da0093505496d8756893e8ac9","first_computed_at":"2026-05-18T03:21:42.979367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:42.979367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JnEVLfq/kUyohkk386w5/9xfk1HF/wuSh8/3f48NuaR5Oj5TAcYVMjHqQa9+d/UKc/YtSHRTiVqT9rzPVBj9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:42.980001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e53938af719b9154068b5528ac7f31b8a796fe4edf74204e24fc6d5d4a94b9","sha256:3505b4eebb1fb85a98e68e8f40797c31c4210de8fa192269b2a7d6f303322776"],"state_sha256":"11c5f4594061f6486575b9fc38b04d32f788faec6d5afa7feda3f11e0f7185ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"662l/iKQxeNToFigivOVhe/B4anfLIoBMit2mEViZjxebFHxXsAYA23FCeDWFlUIkLTH/m0VlugNUKdtG/imDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:55:57.853272Z","bundle_sha256":"7d25db7c6816f7a7729097746f8490dd6366fa7f56d9f3e4baf9ea53c23481e0"}}