{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JTB4PVE7J5EXYXNWFRNZDGX3TV","short_pith_number":"pith:JTB4PVE7","canonical_record":{"source":{"id":"1304.5648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-20T16:35:56Z","cross_cats_sorted":[],"title_canon_sha256":"fb81e5d045e716bb75d06949213101fe60b2948a052146eb9d6628cf3a9e8191","abstract_canon_sha256":"7c33f4441829c8da516d64b23dd16395170547736184ef9a78f96427ea69fee2"},"schema_version":"1.0"},"canonical_sha256":"4cc3c7d49f4f497c5db62c5b919afb9d6126fca121fd480c8e6faa252eb00f8f","source":{"kind":"arxiv","id":"1304.5648","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5648","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5648v2","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5648","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"JTB4PVE7J5EX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JTB4PVE7J5EXYXNW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JTB4PVE7","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JTB4PVE7J5EXYXNWFRNZDGX3TV","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-20T16:35:56Z","cross_cats_sorted":[],"title_canon_sha256":"fb81e5d045e716bb75d06949213101fe60b2948a052146eb9d6628cf3a9e8191","abstract_canon_sha256":"7c33f4441829c8da516d64b23dd16395170547736184ef9a78f96427ea69fee2"},"schema_version":"1.0"},"canonical_sha256":"4cc3c7d49f4f497c5db62c5b919afb9d6126fca121fd480c8e6faa252eb00f8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:14.006668Z","signature_b64":"Dxdlmtd1FRO3g7sy7vvprziMbqDQSYwEaXz4E/VDYWWBty4OGleQYgSGW1XhVaX5oLLdCSWRz6WL6Lcf+tUcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cc3c7d49f4f497c5db62c5b919afb9d6126fca121fd480c8e6faa252eb00f8f","last_reissued_at":"2026-05-18T03:25:14.006026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:14.006026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5648","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":"2026-05-18T03:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eS/s+J0bGakHFJo1FWUlTLBI3waXRUPM4Qsw83WHNYTLdhoP0TUE6v7vtKgVb+zU5EhYCTxJ/pblYWnqfGFfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:06:58.848729Z"},"content_sha256":"cbd7f6fec86b488711d86dad82ddbd53b7bc95e99628f0d787ec69910c3578fd","schema_version":"1.0","event_id":"sha256:cbd7f6fec86b488711d86dad82ddbd53b7bc95e99628f0d787ec69910c3578fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JTB4PVE7J5EXYXNWFRNZDGX3TV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric Powers and Norms of Mackey Functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"John Ullman","submitted_at":"2013-04-20T16:35:56Z","abstract_excerpt":"In this paper we give detailed algebraic descriptions of the derived symmetric power and norm constructions on categories of Mackey functors, as well as the derived G-symmetric monoidal structure. We build on the results of [Ull2], in which it is shown that every Tambara functor over a finite group G arises as the zeroth stable homotopy group of a commutative ring G-spectrum. The norm / restriction adjunctions on categories of Tambara functors promised in [Ull2] are demonstrated algebraically. Finally, we give a new characterization of Tambara functors in terms of multiplicative push forwards "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5648","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":"2026-05-18T03:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jFlYfsRxScr7mTj4g+jgwvufcJ1DvKq7MNdYJfVJRHob3NAdwxULnNnjmjV+MEhTlAD118B5+vg0aY+pWAhODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:06:58.849478Z"},"content_sha256":"427c93c029f89716d260abed84956307068c7920d29a55f59e08b8ac9b6c7c2f","schema_version":"1.0","event_id":"sha256:427c93c029f89716d260abed84956307068c7920d29a55f59e08b8ac9b6c7c2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV/bundle.json","state_url":"https://pith.science/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV/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":"2026-05-31T10:06:58Z","links":{"resolver":"https://pith.science/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV","bundle":"https://pith.science/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV/bundle.json","state":"https://pith.science/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTB4PVE7J5EXYXNWFRNZDGX3TV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JTB4PVE7J5EXYXNWFRNZDGX3TV","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":"7c33f4441829c8da516d64b23dd16395170547736184ef9a78f96427ea69fee2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-20T16:35:56Z","title_canon_sha256":"fb81e5d045e716bb75d06949213101fe60b2948a052146eb9d6628cf3a9e8191"},"schema_version":"1.0","source":{"id":"1304.5648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5648","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5648v2","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5648","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"JTB4PVE7J5EX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JTB4PVE7J5EXYXNW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JTB4PVE7","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:427c93c029f89716d260abed84956307068c7920d29a55f59e08b8ac9b6c7c2f","target":"graph","created_at":"2026-05-18T03:25:14Z","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 give detailed algebraic descriptions of the derived symmetric power and norm constructions on categories of Mackey functors, as well as the derived G-symmetric monoidal structure. We build on the results of [Ull2], in which it is shown that every Tambara functor over a finite group G arises as the zeroth stable homotopy group of a commutative ring G-spectrum. The norm / restriction adjunctions on categories of Tambara functors promised in [Ull2] are demonstrated algebraically. Finally, we give a new characterization of Tambara functors in terms of multiplicative push forwards ","authors_text":"John Ullman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-20T16:35:56Z","title":"Symmetric Powers and Norms of Mackey Functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5648","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:cbd7f6fec86b488711d86dad82ddbd53b7bc95e99628f0d787ec69910c3578fd","target":"record","created_at":"2026-05-18T03:25:14Z","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":"7c33f4441829c8da516d64b23dd16395170547736184ef9a78f96427ea69fee2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-20T16:35:56Z","title_canon_sha256":"fb81e5d045e716bb75d06949213101fe60b2948a052146eb9d6628cf3a9e8191"},"schema_version":"1.0","source":{"id":"1304.5648","kind":"arxiv","version":2}},"canonical_sha256":"4cc3c7d49f4f497c5db62c5b919afb9d6126fca121fd480c8e6faa252eb00f8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cc3c7d49f4f497c5db62c5b919afb9d6126fca121fd480c8e6faa252eb00f8f","first_computed_at":"2026-05-18T03:25:14.006026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:14.006026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dxdlmtd1FRO3g7sy7vvprziMbqDQSYwEaXz4E/VDYWWBty4OGleQYgSGW1XhVaX5oLLdCSWRz6WL6Lcf+tUcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:14.006668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbd7f6fec86b488711d86dad82ddbd53b7bc95e99628f0d787ec69910c3578fd","sha256:427c93c029f89716d260abed84956307068c7920d29a55f59e08b8ac9b6c7c2f"],"state_sha256":"777ecdcae6cc92d940f987c045f715dd37ca4091e8002bd56a4deac37abaa1a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZmFHIdB/c+/GF867+UCd/cC+BRQi/Qh670uwq/OUhZvmz6DHGVntyeXrAmGDdb2Ile3kPjkDUBA7XSgTnVwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:06:58.852520Z","bundle_sha256":"e5edfc2f46835631248a19c0b1e79c61b4ff8745fcc145f741751df872763e09"}}