{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OI6Z2NJRGPHXPSFBND4FTZKAX2","short_pith_number":"pith:OI6Z2NJR","canonical_record":{"source":{"id":"2502.13882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-19T17:06:47Z","cross_cats_sorted":["math.AT","math.RT"],"title_canon_sha256":"033ee84372b064c381528fced678722cefb7bee0489a33f6c44d73b71f48d03b","abstract_canon_sha256":"346d5a695d2e0c8af8481ba450844a1abcd9c56907c09914816b0de292476b17"},"schema_version":"1.0"},"canonical_sha256":"723d9d353133cf77c8a168f859e540bea7e287db95eb23cacbe11b07ed9b8628","source":{"kind":"arxiv","id":"2502.13882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13882","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13882v1","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13882","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"OI6Z2NJRGPHX","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"pith_short_16","alias_value":"OI6Z2NJRGPHXPSFB","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"pith_short_8","alias_value":"OI6Z2NJR","created_at":"2026-07-05T10:17:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OI6Z2NJRGPHXPSFBND4FTZKAX2","target":"record","payload":{"canonical_record":{"source":{"id":"2502.13882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-19T17:06:47Z","cross_cats_sorted":["math.AT","math.RT"],"title_canon_sha256":"033ee84372b064c381528fced678722cefb7bee0489a33f6c44d73b71f48d03b","abstract_canon_sha256":"346d5a695d2e0c8af8481ba450844a1abcd9c56907c09914816b0de292476b17"},"schema_version":"1.0"},"canonical_sha256":"723d9d353133cf77c8a168f859e540bea7e287db95eb23cacbe11b07ed9b8628","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:17:01.961030Z","signature_b64":"+7YGWVaG4YDtUOjEtD9OY8SbeG9D3yHR7u4vazK0BESfu5/ur3KSARQAsyOhAVzeDJ0sWBx0eRu0aOQvVDyCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"723d9d353133cf77c8a168f859e540bea7e287db95eb23cacbe11b07ed9b8628","last_reissued_at":"2026-07-05T10:17:01.960626Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:17:01.960626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.13882","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":"2026-07-05T10:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4ILKwvfruQitbr98aKpuXEqhaVE8wvaHsujCiWjkL6v5R9odfbOGJzAd6hJLVqaz3WoWyLNf+LdFO1nqRzyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:42:18.370460Z"},"content_sha256":"7615380fad4a3973014820cd9dcf1c38f9be19e9c23bdb0a37fcdcc6efc1e5bc","schema_version":"1.0","event_id":"sha256:7615380fad4a3973014820cd9dcf1c38f9be19e9c23bdb0a37fcdcc6efc1e5bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OI6Z2NJRGPHXPSFBND4FTZKAX2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic loop spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AG","authors_text":"Adeel A. Khan, Emile Bouaziz","submitted_at":"2025-02-19T17:06:47Z","abstract_excerpt":"We introduce an elliptic avatar of loop spaces in derived algebraic geometry, completing the familiar trichotomoy of rational, trigonometric and elliptic objects. Heuristically, the elliptic loop space of $\\mathcal{Y}$ is the stack of maps to $\\mathcal{Y}$ from a certain exotic avatar $\\mathcal{S}_{E}$ of the elliptic curve $E$, such that the category of quasi-coherent sheaves on $\\mathcal{S}_{E}$ is the convolution category of zero-dimensionally supported coherent sheaves on $E$. For quotient stacks, the structure sheaf of the elliptic loop space gives rise to a theory of equivariant elliptic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13882","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/2502.13882/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":"2026-07-05T10:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djUNhNU3Sh/+jhPNQKU/sv7gtm+gJW4U+z4LQhR3MbHWUuikamgjiCwtNIlSRqKXbQVDEXXYkMjSBBgS9fudAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:42:18.371368Z"},"content_sha256":"a8e5092f386a920af91f60031b2c14d9f44a58f7fdbbc716d3294156930d1106","schema_version":"1.0","event_id":"sha256:a8e5092f386a920af91f60031b2c14d9f44a58f7fdbbc716d3294156930d1106"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2/bundle.json","state_url":"https://pith.science/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2/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":"2026-08-17T21:42:18Z","links":{"resolver":"https://pith.science/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2","bundle":"https://pith.science/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2/bundle.json","state":"https://pith.science/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OI6Z2NJRGPHXPSFBND4FTZKAX2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OI6Z2NJRGPHXPSFBND4FTZKAX2","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":"346d5a695d2e0c8af8481ba450844a1abcd9c56907c09914816b0de292476b17","cross_cats_sorted":["math.AT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-19T17:06:47Z","title_canon_sha256":"033ee84372b064c381528fced678722cefb7bee0489a33f6c44d73b71f48d03b"},"schema_version":"1.0","source":{"id":"2502.13882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13882","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13882v1","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13882","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"OI6Z2NJRGPHX","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"pith_short_16","alias_value":"OI6Z2NJRGPHXPSFB","created_at":"2026-07-05T10:17:01Z"},{"alias_kind":"pith_short_8","alias_value":"OI6Z2NJR","created_at":"2026-07-05T10:17:01Z"}],"graph_snapshots":[{"event_id":"sha256:a8e5092f386a920af91f60031b2c14d9f44a58f7fdbbc716d3294156930d1106","target":"graph","created_at":"2026-07-05T10:17:01Z","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/2502.13882/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce an elliptic avatar of loop spaces in derived algebraic geometry, completing the familiar trichotomoy of rational, trigonometric and elliptic objects. Heuristically, the elliptic loop space of $\\mathcal{Y}$ is the stack of maps to $\\mathcal{Y}$ from a certain exotic avatar $\\mathcal{S}_{E}$ of the elliptic curve $E$, such that the category of quasi-coherent sheaves on $\\mathcal{S}_{E}$ is the convolution category of zero-dimensionally supported coherent sheaves on $E$. For quotient stacks, the structure sheaf of the elliptic loop space gives rise to a theory of equivariant elliptic","authors_text":"Adeel A. Khan, Emile Bouaziz","cross_cats":["math.AT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-19T17:06:47Z","title":"Elliptic loop spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13882","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":"sha256:7615380fad4a3973014820cd9dcf1c38f9be19e9c23bdb0a37fcdcc6efc1e5bc","target":"record","created_at":"2026-07-05T10:17:01Z","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":"346d5a695d2e0c8af8481ba450844a1abcd9c56907c09914816b0de292476b17","cross_cats_sorted":["math.AT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-19T17:06:47Z","title_canon_sha256":"033ee84372b064c381528fced678722cefb7bee0489a33f6c44d73b71f48d03b"},"schema_version":"1.0","source":{"id":"2502.13882","kind":"arxiv","version":1}},"canonical_sha256":"723d9d353133cf77c8a168f859e540bea7e287db95eb23cacbe11b07ed9b8628","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"723d9d353133cf77c8a168f859e540bea7e287db95eb23cacbe11b07ed9b8628","first_computed_at":"2026-07-05T10:17:01.960626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:17:01.960626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+7YGWVaG4YDtUOjEtD9OY8SbeG9D3yHR7u4vazK0BESfu5/ur3KSARQAsyOhAVzeDJ0sWBx0eRu0aOQvVDyCBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:17:01.961030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.13882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7615380fad4a3973014820cd9dcf1c38f9be19e9c23bdb0a37fcdcc6efc1e5bc","sha256:a8e5092f386a920af91f60031b2c14d9f44a58f7fdbbc716d3294156930d1106"],"state_sha256":"baae234a6e0afef62b134d161bd4120345e6216adfeb1c86e1d0742b1552a456"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1dF6XXspuGZXJEdd+y7mK/PI1m2z2Im/YNK3AGH0f8xtFwMvRnAvAgUo07tixpHsUMHIJh0CKD8PQ0Xh9vRKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T21:42:18.376935Z","bundle_sha256":"9696a28f8d7fc3b5c1f8d83a4b82143231a28557ccc63303e64cbc3e2267a931"}}