{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:K2ZNT4QOH76CUIIT7DNVC3267A","short_pith_number":"pith:K2ZNT4QO","canonical_record":{"source":{"id":"1306.1753","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-07T15:49:52Z","cross_cats_sorted":[],"title_canon_sha256":"86e98fd74eeafce0a6fd04f85343e161236082dfdea5a94bd25057667e16b098","abstract_canon_sha256":"4563c1b4081df1f2dde6681cfbe25a4ef40182d32d31171da5a96e39e9bddfa7"},"schema_version":"1.0"},"canonical_sha256":"56b2d9f20e3ffc2a2113f8db516f5ef82726aefedac648d7c3fb49a90260c64e","source":{"kind":"arxiv","id":"1306.1753","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1753","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1753v2","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1753","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"K2ZNT4QOH76C","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K2ZNT4QOH76CUIIT","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K2ZNT4QO","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:K2ZNT4QOH76CUIIT7DNVC3267A","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1753","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-07T15:49:52Z","cross_cats_sorted":[],"title_canon_sha256":"86e98fd74eeafce0a6fd04f85343e161236082dfdea5a94bd25057667e16b098","abstract_canon_sha256":"4563c1b4081df1f2dde6681cfbe25a4ef40182d32d31171da5a96e39e9bddfa7"},"schema_version":"1.0"},"canonical_sha256":"56b2d9f20e3ffc2a2113f8db516f5ef82726aefedac648d7c3fb49a90260c64e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:23.169336Z","signature_b64":"ObwfpAmfNefM5U9TPLQEKNtLDp0EYS4SaVp4i0LtwIN7SznDA7Si1hoI2utjiKtkjOIcvmm1CvjJb00bl198Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56b2d9f20e3ffc2a2113f8db516f5ef82726aefedac648d7c3fb49a90260c64e","last_reissued_at":"2026-05-18T03:21:23.168758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:23.168758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1753","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":"2026-05-18T03:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpP62McYunNWDefUtLgm8SGlv1frB7dKfgqGzs69Nnsj7ykksEgsHYmJw7ZE1XjMGVLYMI/vmJWjuNPGO/kmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:59:27.440833Z"},"content_sha256":"3d20d858b582f639a3cb5130b620af4266f492c3c7891b811d4f0ee19dc4d032","schema_version":"1.0","event_id":"sha256:3d20d858b582f639a3cb5130b620af4266f492c3c7891b811d4f0ee19dc4d032"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:K2ZNT4QOH76CUIIT7DNVC3267A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Charged Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"John R. Klein, John W. Peter","submitted_at":"2013-06-07T15:49:52Z","abstract_excerpt":"A charged space is a space equipped with two distinct base points. Such spaces arise as the unreduced suspension of an unbased space. More generally, one can work in the fiberwise setting over a fixed space B. A fiberwise charged space over B is a space X equipped with map to B and having two sections. One can ask whether or not a fiberwise charged space over B is a fiberwise suspension. We answer this question in a certain metastable range by producing a necessary and sufficient obstruction. As an application we show how this can be used to study when an embedding into a smooth manifold of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1753","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":"2026-05-18T03:21:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kL6faqASRkfExuooQ3D98dt4Qhvh9b5z3wGOpQyUiiojOMlcO+jWayytDnFI6sJYaKaHH8imJ0htvlTLm72YBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:59:27.441598Z"},"content_sha256":"64535625d4ee06748eb660b4404ec0d7cf410bf7ed1ee5e1089cce489e6d28ed","schema_version":"1.0","event_id":"sha256:64535625d4ee06748eb660b4404ec0d7cf410bf7ed1ee5e1089cce489e6d28ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2ZNT4QOH76CUIIT7DNVC3267A/bundle.json","state_url":"https://pith.science/pith/K2ZNT4QOH76CUIIT7DNVC3267A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2ZNT4QOH76CUIIT7DNVC3267A/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":"2026-06-06T15:59:27Z","links":{"resolver":"https://pith.science/pith/K2ZNT4QOH76CUIIT7DNVC3267A","bundle":"https://pith.science/pith/K2ZNT4QOH76CUIIT7DNVC3267A/bundle.json","state":"https://pith.science/pith/K2ZNT4QOH76CUIIT7DNVC3267A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2ZNT4QOH76CUIIT7DNVC3267A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:K2ZNT4QOH76CUIIT7DNVC3267A","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":"4563c1b4081df1f2dde6681cfbe25a4ef40182d32d31171da5a96e39e9bddfa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-07T15:49:52Z","title_canon_sha256":"86e98fd74eeafce0a6fd04f85343e161236082dfdea5a94bd25057667e16b098"},"schema_version":"1.0","source":{"id":"1306.1753","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1753","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1753v2","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1753","created_at":"2026-05-18T03:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"K2ZNT4QOH76C","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K2ZNT4QOH76CUIIT","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K2ZNT4QO","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:64535625d4ee06748eb660b4404ec0d7cf410bf7ed1ee5e1089cce489e6d28ed","target":"graph","created_at":"2026-05-18T03:21:23Z","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":"A charged space is a space equipped with two distinct base points. Such spaces arise as the unreduced suspension of an unbased space. More generally, one can work in the fiberwise setting over a fixed space B. A fiberwise charged space over B is a space X equipped with map to B and having two sections. One can ask whether or not a fiberwise charged space over B is a fiberwise suspension. We answer this question in a certain metastable range by producing a necessary and sufficient obstruction. As an application we show how this can be used to study when an embedding into a smooth manifold of th","authors_text":"John R. Klein, John W. Peter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-07T15:49:52Z","title":"Charged Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1753","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":"sha256:3d20d858b582f639a3cb5130b620af4266f492c3c7891b811d4f0ee19dc4d032","target":"record","created_at":"2026-05-18T03:21:23Z","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":"4563c1b4081df1f2dde6681cfbe25a4ef40182d32d31171da5a96e39e9bddfa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-06-07T15:49:52Z","title_canon_sha256":"86e98fd74eeafce0a6fd04f85343e161236082dfdea5a94bd25057667e16b098"},"schema_version":"1.0","source":{"id":"1306.1753","kind":"arxiv","version":2}},"canonical_sha256":"56b2d9f20e3ffc2a2113f8db516f5ef82726aefedac648d7c3fb49a90260c64e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56b2d9f20e3ffc2a2113f8db516f5ef82726aefedac648d7c3fb49a90260c64e","first_computed_at":"2026-05-18T03:21:23.168758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:23.168758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ObwfpAmfNefM5U9TPLQEKNtLDp0EYS4SaVp4i0LtwIN7SznDA7Si1hoI2utjiKtkjOIcvmm1CvjJb00bl198Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:23.169336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1753","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d20d858b582f639a3cb5130b620af4266f492c3c7891b811d4f0ee19dc4d032","sha256:64535625d4ee06748eb660b4404ec0d7cf410bf7ed1ee5e1089cce489e6d28ed"],"state_sha256":"1a75e68a1b81dd57af83e9401579994b2c01960832817ca76c621818c33db0b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9md3rdHsF6rYLedB3wmVr/C65GHJV/M6ld9D9W89zARavv4pAkXo+oFWiqYukFdqggcP9vKNCivyUZ0nVCLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:59:27.445222Z","bundle_sha256":"885764a0be8c942a196f5a7ac61e438cf5d95b42814e3163031ffc8b9b8bbca1"}}