{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SIPOQH5OBN6RX4SYJONGGURYU5","short_pith_number":"pith:SIPOQH5O","canonical_record":{"source":{"id":"1012.1264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-06T18:06:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f04045504bdc550766abb86cbf018867dfff962b1d3c6fdab2b70721d44550a8","abstract_canon_sha256":"a1f6a7551314531217f0013f5dd23e52997dc012f97a81ac26681bce6eeac7df"},"schema_version":"1.0"},"canonical_sha256":"921ee81fae0b7d1bf2584b9a635238a74ba266543aca9fc5ea1779635d552a47","source":{"kind":"arxiv","id":"1012.1264","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1264","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1264v2","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1264","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"SIPOQH5OBN6R","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SIPOQH5OBN6RX4SY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SIPOQH5O","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SIPOQH5OBN6RX4SYJONGGURYU5","target":"record","payload":{"canonical_record":{"source":{"id":"1012.1264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-06T18:06:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f04045504bdc550766abb86cbf018867dfff962b1d3c6fdab2b70721d44550a8","abstract_canon_sha256":"a1f6a7551314531217f0013f5dd23e52997dc012f97a81ac26681bce6eeac7df"},"schema_version":"1.0"},"canonical_sha256":"921ee81fae0b7d1bf2584b9a635238a74ba266543aca9fc5ea1779635d552a47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:38.538920Z","signature_b64":"yWXJ0BD1/gMVJnA4xuab0h+fqzfGJpbRFG5zNdy5Rnwp8MBY2s2zRHIksenaW6OEl+qWsp2rJzqfLNBbaIALAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"921ee81fae0b7d1bf2584b9a635238a74ba266543aca9fc5ea1779635d552a47","last_reissued_at":"2026-05-18T04:33:38.538395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:38.538395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.1264","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":"2026-05-18T04:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IC95XucFnNOd/cIIBDtEWOjGVlF5FFquaX0MlZ1zlKD8CoBKGyAYDPeb3myAz0Izj1ZNrJkwjkGP3HIMF/xYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:03.674878Z"},"content_sha256":"9e26ff267563611457aba4d2921d9163d81ffe642b2f65ea8ac20920a9e634a8","schema_version":"1.0","event_id":"sha256:9e26ff267563611457aba4d2921d9163d81ffe642b2f65ea8ac20920a9e634a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SIPOQH5OBN6RX4SYJONGGURYU5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Another viewpoint on J-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Markus Spitzweck","submitted_at":"2010-12-06T18:06:28Z","abstract_excerpt":"We give an interpretation of J-spaces in terms of symmetric spectra in symmetric sequences. As application we show how one can define graded endomorphism objects in a general situation. As example we discuss the motivic bigraded endomorphisms of a motivic E-infinity ring spectrum. Finally we give an infinity categorical interpretation of our result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1264","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":"2026-05-18T04:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PN3Q8oB826iMcbfRzC0yas9kBSns/sgCRvHmXLGK8pkpB99VA6RCJkC4HnT7NHGE3jUkb30UvdQxtldZ5kniCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:03.675416Z"},"content_sha256":"50b6e0be60f28533751b2d56f1da17ecfe72f7e44ae0f6fdc93956fed27c569e","schema_version":"1.0","event_id":"sha256:50b6e0be60f28533751b2d56f1da17ecfe72f7e44ae0f6fdc93956fed27c569e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIPOQH5OBN6RX4SYJONGGURYU5/bundle.json","state_url":"https://pith.science/pith/SIPOQH5OBN6RX4SYJONGGURYU5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIPOQH5OBN6RX4SYJONGGURYU5/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":"2026-05-26T13:46:03Z","links":{"resolver":"https://pith.science/pith/SIPOQH5OBN6RX4SYJONGGURYU5","bundle":"https://pith.science/pith/SIPOQH5OBN6RX4SYJONGGURYU5/bundle.json","state":"https://pith.science/pith/SIPOQH5OBN6RX4SYJONGGURYU5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIPOQH5OBN6RX4SYJONGGURYU5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SIPOQH5OBN6RX4SYJONGGURYU5","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":"a1f6a7551314531217f0013f5dd23e52997dc012f97a81ac26681bce6eeac7df","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-06T18:06:28Z","title_canon_sha256":"f04045504bdc550766abb86cbf018867dfff962b1d3c6fdab2b70721d44550a8"},"schema_version":"1.0","source":{"id":"1012.1264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1264","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1264v2","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1264","created_at":"2026-05-18T04:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"SIPOQH5OBN6R","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SIPOQH5OBN6RX4SY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SIPOQH5O","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:50b6e0be60f28533751b2d56f1da17ecfe72f7e44ae0f6fdc93956fed27c569e","target":"graph","created_at":"2026-05-18T04:33:38Z","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":"We give an interpretation of J-spaces in terms of symmetric spectra in symmetric sequences. As application we show how one can define graded endomorphism objects in a general situation. As example we discuss the motivic bigraded endomorphisms of a motivic E-infinity ring spectrum. Finally we give an infinity categorical interpretation of our result.","authors_text":"Markus Spitzweck","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-06T18:06:28Z","title":"Another viewpoint on J-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1264","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":"sha256:9e26ff267563611457aba4d2921d9163d81ffe642b2f65ea8ac20920a9e634a8","target":"record","created_at":"2026-05-18T04:33:38Z","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":"a1f6a7551314531217f0013f5dd23e52997dc012f97a81ac26681bce6eeac7df","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-12-06T18:06:28Z","title_canon_sha256":"f04045504bdc550766abb86cbf018867dfff962b1d3c6fdab2b70721d44550a8"},"schema_version":"1.0","source":{"id":"1012.1264","kind":"arxiv","version":2}},"canonical_sha256":"921ee81fae0b7d1bf2584b9a635238a74ba266543aca9fc5ea1779635d552a47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"921ee81fae0b7d1bf2584b9a635238a74ba266543aca9fc5ea1779635d552a47","first_computed_at":"2026-05-18T04:33:38.538395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:38.538395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yWXJ0BD1/gMVJnA4xuab0h+fqzfGJpbRFG5zNdy5Rnwp8MBY2s2zRHIksenaW6OEl+qWsp2rJzqfLNBbaIALAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:38.538920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e26ff267563611457aba4d2921d9163d81ffe642b2f65ea8ac20920a9e634a8","sha256:50b6e0be60f28533751b2d56f1da17ecfe72f7e44ae0f6fdc93956fed27c569e"],"state_sha256":"0bb1875dafe153011cdf754dd3662e7efe59d045e2ba8a0b7e0dd7502cac810e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfpGpIqP+rHi6WxtSyehWWvkmI8z4l8HtA8axFK2reVju5p3/GmHLUyiE37Vxq/x7Ge8i2BukjZi57acFFabBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:46:03.678266Z","bundle_sha256":"688631ec390080c320f01f4058e0ef06bc2e5d35a72467c0e161dca16b127c49"}}