{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5HM3ZAHJILKQDJ2UDDK6SGBNBV","short_pith_number":"pith:5HM3ZAHJ","canonical_record":{"source":{"id":"1203.2460","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2012-03-12T11:52:40Z","cross_cats_sorted":[],"title_canon_sha256":"30ba6bab25e551a73ff07a0edd7b7f77bb7cac4fcb0db1390df70e622181324b","abstract_canon_sha256":"3990a59020d4ab6a43565ec88fd82375adb42c912e858391541161bd541e374b"},"schema_version":"1.0"},"canonical_sha256":"e9d9bc80e942d501a75418d5e9182d0d4c13eac602dc12d1e589991f86ac71b0","source":{"kind":"arxiv","id":"1203.2460","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2460","created_at":"2026-05-18T01:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2460v4","created_at":"2026-05-18T01:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2460","created_at":"2026-05-18T01:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"5HM3ZAHJILKQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5HM3ZAHJILKQDJ2U","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5HM3ZAHJ","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5HM3ZAHJILKQDJ2UDDK6SGBNBV","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2460","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2012-03-12T11:52:40Z","cross_cats_sorted":[],"title_canon_sha256":"30ba6bab25e551a73ff07a0edd7b7f77bb7cac4fcb0db1390df70e622181324b","abstract_canon_sha256":"3990a59020d4ab6a43565ec88fd82375adb42c912e858391541161bd541e374b"},"schema_version":"1.0"},"canonical_sha256":"e9d9bc80e942d501a75418d5e9182d0d4c13eac602dc12d1e589991f86ac71b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:30.075641Z","signature_b64":"j7xSaZC9gtJN/prkg1RPgVZorH+Z/YyyF7UtE90o2UR4m5M1yM6n1JiDWyHvSaGIdaTTOSLx1WQjhmEs1aE8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9d9bc80e942d501a75418d5e9182d0d4c13eac602dc12d1e589991f86ac71b0","last_reissued_at":"2026-05-18T01:16:30.075192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:30.075192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2460","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hR0VBnPwbm5KIwyo2MzRb4/hns+UWfxqD5f+2R/FwU3sCGh1D5K3JDkQCJzhRCNbylJzo/2/cNDsT1YKTlgqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:42:48.384816Z"},"content_sha256":"63fafed95698c7572dc5c497a4863eecac3b8dcb87443734e820b2a439892abc","schema_version":"1.0","event_id":"sha256:63fafed95698c7572dc5c497a4863eecac3b8dcb87443734e820b2a439892abc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5HM3ZAHJILKQDJ2UDDK6SGBNBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplicial principal bundles in parametrized spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Danny Stevenson, David Michael Roberts","submitted_at":"2012-03-12T11:52:40Z","abstract_excerpt":"In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we construct a product-preserving classifying space functor for groups in the category of spaces over a fixed space B. Additionally, we prove that the fiberwise geometric realization functor sends a large class of simplicial parametrized principal bundles to ordinary parametrized principal bundles. As an application we show that the fiberwise geometric realization of the universal simplicial principal bundle for a simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2460","kind":"arxiv","version":4},"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":"2026-05-18T01:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"He37qtkVaqajx8HNNmpuZmIPykwfSR6sLWmfv4YMgFJz32hnuGSmvXaOCfVGjrRH5cfh27aX8iSVdTLqKlFdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:42:48.385152Z"},"content_sha256":"600fba91cb9f51346f33dfe8b5b329c5c533fb417a7a66f9b4537a807957c9d4","schema_version":"1.0","event_id":"sha256:600fba91cb9f51346f33dfe8b5b329c5c533fb417a7a66f9b4537a807957c9d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV/bundle.json","state_url":"https://pith.science/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV/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":"2026-06-04T15:42:48Z","links":{"resolver":"https://pith.science/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV","bundle":"https://pith.science/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV/bundle.json","state":"https://pith.science/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HM3ZAHJILKQDJ2UDDK6SGBNBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5HM3ZAHJILKQDJ2UDDK6SGBNBV","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":"3990a59020d4ab6a43565ec88fd82375adb42c912e858391541161bd541e374b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2012-03-12T11:52:40Z","title_canon_sha256":"30ba6bab25e551a73ff07a0edd7b7f77bb7cac4fcb0db1390df70e622181324b"},"schema_version":"1.0","source":{"id":"1203.2460","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2460","created_at":"2026-05-18T01:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2460v4","created_at":"2026-05-18T01:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2460","created_at":"2026-05-18T01:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"5HM3ZAHJILKQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5HM3ZAHJILKQDJ2U","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5HM3ZAHJ","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:600fba91cb9f51346f33dfe8b5b329c5c533fb417a7a66f9b4537a807957c9d4","target":"graph","created_at":"2026-05-18T01:16:30Z","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 the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we construct a product-preserving classifying space functor for groups in the category of spaces over a fixed space B. Additionally, we prove that the fiberwise geometric realization functor sends a large class of simplicial parametrized principal bundles to ordinary parametrized principal bundles. As an application we show that the fiberwise geometric realization of the universal simplicial principal bundle for a simp","authors_text":"Danny Stevenson, David Michael Roberts","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2012-03-12T11:52:40Z","title":"Simplicial principal bundles in parametrized spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2460","kind":"arxiv","version":4},"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":"sha256:63fafed95698c7572dc5c497a4863eecac3b8dcb87443734e820b2a439892abc","target":"record","created_at":"2026-05-18T01:16:30Z","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":"3990a59020d4ab6a43565ec88fd82375adb42c912e858391541161bd541e374b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2012-03-12T11:52:40Z","title_canon_sha256":"30ba6bab25e551a73ff07a0edd7b7f77bb7cac4fcb0db1390df70e622181324b"},"schema_version":"1.0","source":{"id":"1203.2460","kind":"arxiv","version":4}},"canonical_sha256":"e9d9bc80e942d501a75418d5e9182d0d4c13eac602dc12d1e589991f86ac71b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9d9bc80e942d501a75418d5e9182d0d4c13eac602dc12d1e589991f86ac71b0","first_computed_at":"2026-05-18T01:16:30.075192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:30.075192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j7xSaZC9gtJN/prkg1RPgVZorH+Z/YyyF7UtE90o2UR4m5M1yM6n1JiDWyHvSaGIdaTTOSLx1WQjhmEs1aE8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:30.075641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2460","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63fafed95698c7572dc5c497a4863eecac3b8dcb87443734e820b2a439892abc","sha256:600fba91cb9f51346f33dfe8b5b329c5c533fb417a7a66f9b4537a807957c9d4"],"state_sha256":"b47cc370314bd00c256fd5cc0ecfa9503fe96309cc8fefd4e2042105e3b031f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNaOIi2S7LyVxjDMJrkOuEMlw90ONf3JQqkNyIaICi9ulEVn/sKaBZcd+oGm9gvd2GYW9AJZjb6ACTv01s/nBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:42:48.387047Z","bundle_sha256":"097d033057f08cadc5dcfd669a9252e9c68d97edd7b91afe24e54d0603556d64"}}