{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:RXF23GVBU5B2L57T7OE5J7MM5G","short_pith_number":"pith:RXF23GVB","canonical_record":{"source":{"id":"2102.06724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2021-02-12T19:09:56Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"a22d93ce6994bf14312b5e056e99032f93949d8e7b3bb2cf69adc5a990d0c5a2","abstract_canon_sha256":"dbc4d958982b4630b20f07e5d2daff4f7537c54f5f39846a5b18f40245b5efc0"},"schema_version":"1.0"},"canonical_sha256":"8dcbad9aa1a743a5f7f3fb89d4fd8ce9a7f9ffe5decec84373885eae198dd444","source":{"kind":"arxiv","id":"2102.06724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06724","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06724v1","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06724","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"RXF23GVBU5B2","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"pith_short_16","alias_value":"RXF23GVBU5B2L57T","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"pith_short_8","alias_value":"RXF23GVB","created_at":"2026-07-05T02:14:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:RXF23GVBU5B2L57T7OE5J7MM5G","target":"record","payload":{"canonical_record":{"source":{"id":"2102.06724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2021-02-12T19:09:56Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"a22d93ce6994bf14312b5e056e99032f93949d8e7b3bb2cf69adc5a990d0c5a2","abstract_canon_sha256":"dbc4d958982b4630b20f07e5d2daff4f7537c54f5f39846a5b18f40245b5efc0"},"schema_version":"1.0"},"canonical_sha256":"8dcbad9aa1a743a5f7f3fb89d4fd8ce9a7f9ffe5decec84373885eae198dd444","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:57.725597Z","signature_b64":"t68cyBBP0JhCwFGzIHyHv/klWtylovZtlYj66IsAH1khJQr8w8/csuKLW4VXMxO7M+gZxhqGUKyFyOuAWIRZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dcbad9aa1a743a5f7f3fb89d4fd8ce9a7f9ffe5decec84373885eae198dd444","last_reissued_at":"2026-07-05T02:14:57.725103Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:57.725103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.06724","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Trmd6zUGy8dhFsVKIfZPg76QgjEQQbsaRmI0j93o1SYzMaTBOS8OmyHy96sDqsTu2yGZ1ckLmcZTK3gFPbdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:24:31.515164Z"},"content_sha256":"1f787ea5198104f16a616448b29f8f73b9717ca1d5446a5bf799d6233b2d5c4f","schema_version":"1.0","event_id":"sha256:1f787ea5198104f16a616448b29f8f73b9717ca1d5446a5bf799d6233b2d5c4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:RXF23GVBU5B2L57T7OE5J7MM5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy Mackey functors of equivariant algebraic $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.AT","authors_text":"Thomas Brazelton","submitted_at":"2021-02-12T19:09:56Z","abstract_excerpt":"Given a finite group $G$ acting on a ring $R$, Merling constructed an equivariant algebraic $K$-theory $G$-spectrum, and work of Malkiewich and Merling, as well as work of Barwick, provides an interpretation of this construction as a spectral Mackey functor. This construction is powerful, but highly categorical; as a result the Mackey functors comprising the homotopy are not obvious from the construction and have therefore not yet been calculated. In this work, we provide a computation of the homotopy Mackey functors of equivariant algebraic $K$-theory in terms of a purely algebraic constructi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06724","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.06724/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:14:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"345vzdtbhhRrw6ryebslzcs4WodJJLdLpbwUV+Ktbqesu2099BrVxVgB2EarnOhtHfNNt50Clk1YBzscNTIZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:24:31.515544Z"},"content_sha256":"0d4cacd08466d207fc2894483e1af4e145dd0b00f2069602f0ad3ce914ff50dd","schema_version":"1.0","event_id":"sha256:0d4cacd08466d207fc2894483e1af4e145dd0b00f2069602f0ad3ce914ff50dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXF23GVBU5B2L57T7OE5J7MM5G/bundle.json","state_url":"https://pith.science/pith/RXF23GVBU5B2L57T7OE5J7MM5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXF23GVBU5B2L57T7OE5J7MM5G/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":"2026-07-07T12:24:31Z","links":{"resolver":"https://pith.science/pith/RXF23GVBU5B2L57T7OE5J7MM5G","bundle":"https://pith.science/pith/RXF23GVBU5B2L57T7OE5J7MM5G/bundle.json","state":"https://pith.science/pith/RXF23GVBU5B2L57T7OE5J7MM5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXF23GVBU5B2L57T7OE5J7MM5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:RXF23GVBU5B2L57T7OE5J7MM5G","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":"dbc4d958982b4630b20f07e5d2daff4f7537c54f5f39846a5b18f40245b5efc0","cross_cats_sorted":["math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2021-02-12T19:09:56Z","title_canon_sha256":"a22d93ce6994bf14312b5e056e99032f93949d8e7b3bb2cf69adc5a990d0c5a2"},"schema_version":"1.0","source":{"id":"2102.06724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.06724","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"arxiv_version","alias_value":"2102.06724v1","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.06724","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"pith_short_12","alias_value":"RXF23GVBU5B2","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"pith_short_16","alias_value":"RXF23GVBU5B2L57T","created_at":"2026-07-05T02:14:57Z"},{"alias_kind":"pith_short_8","alias_value":"RXF23GVB","created_at":"2026-07-05T02:14:57Z"}],"graph_snapshots":[{"event_id":"sha256:0d4cacd08466d207fc2894483e1af4e145dd0b00f2069602f0ad3ce914ff50dd","target":"graph","created_at":"2026-07-05T02:14:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.06724/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a finite group $G$ acting on a ring $R$, Merling constructed an equivariant algebraic $K$-theory $G$-spectrum, and work of Malkiewich and Merling, as well as work of Barwick, provides an interpretation of this construction as a spectral Mackey functor. This construction is powerful, but highly categorical; as a result the Mackey functors comprising the homotopy are not obvious from the construction and have therefore not yet been calculated. In this work, we provide a computation of the homotopy Mackey functors of equivariant algebraic $K$-theory in terms of a purely algebraic constructi","authors_text":"Thomas Brazelton","cross_cats":["math.KT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2021-02-12T19:09:56Z","title":"Homotopy Mackey functors of equivariant algebraic $K$-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.06724","kind":"arxiv","version":1},"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":"sha256:1f787ea5198104f16a616448b29f8f73b9717ca1d5446a5bf799d6233b2d5c4f","target":"record","created_at":"2026-07-05T02:14:57Z","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":"dbc4d958982b4630b20f07e5d2daff4f7537c54f5f39846a5b18f40245b5efc0","cross_cats_sorted":["math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2021-02-12T19:09:56Z","title_canon_sha256":"a22d93ce6994bf14312b5e056e99032f93949d8e7b3bb2cf69adc5a990d0c5a2"},"schema_version":"1.0","source":{"id":"2102.06724","kind":"arxiv","version":1}},"canonical_sha256":"8dcbad9aa1a743a5f7f3fb89d4fd8ce9a7f9ffe5decec84373885eae198dd444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dcbad9aa1a743a5f7f3fb89d4fd8ce9a7f9ffe5decec84373885eae198dd444","first_computed_at":"2026-07-05T02:14:57.725103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:57.725103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t68cyBBP0JhCwFGzIHyHv/klWtylovZtlYj66IsAH1khJQr8w8/csuKLW4VXMxO7M+gZxhqGUKyFyOuAWIRZBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:57.725597Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.06724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f787ea5198104f16a616448b29f8f73b9717ca1d5446a5bf799d6233b2d5c4f","sha256:0d4cacd08466d207fc2894483e1af4e145dd0b00f2069602f0ad3ce914ff50dd"],"state_sha256":"8166ee7cecbdecd5685c4e56fb7e7004d9c5172bedcee1bbdd7bb64f86e05a7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zc7XqMBcGvy62rcIdip8zBxTBu8w4i/4aL1rl0b6rjdJq+TPuGT2inH5qs0tGsxNHkQGxUFgS6o0C8NCcQHTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:24:31.517686Z","bundle_sha256":"6aca6fa5fe29623a0ff2649283d19e63c0157e5515333957ab2629afc4a84766"}}