{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QBXLWFAQ2VKYPZFJCJYNMUD4QC","short_pith_number":"pith:QBXLWFAQ","canonical_record":{"source":{"id":"2607.00496","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:25:31Z","cross_cats_sorted":[],"title_canon_sha256":"17138ba838fb65f10e9f6c26b433e41f5870b3b7173137442b08ea86a1111f38","abstract_canon_sha256":"8057953b22314aa9efc8d794ef6e97358d22333f57f81581b18031bb4c1c0850"},"schema_version":"1.0"},"canonical_sha256":"806ebb1410d55587e4a91270d6507c80bae48067e957dbe07f1331c1b0c1087c","source":{"kind":"arxiv","id":"2607.00496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00496","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00496v1","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00496","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"QBXLWFAQ2VKY","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"QBXLWFAQ2VKYPZFJ","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"QBXLWFAQ","created_at":"2026-07-02T01:17:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QBXLWFAQ2VKYPZFJCJYNMUD4QC","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00496","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:25:31Z","cross_cats_sorted":[],"title_canon_sha256":"17138ba838fb65f10e9f6c26b433e41f5870b3b7173137442b08ea86a1111f38","abstract_canon_sha256":"8057953b22314aa9efc8d794ef6e97358d22333f57f81581b18031bb4c1c0850"},"schema_version":"1.0"},"canonical_sha256":"806ebb1410d55587e4a91270d6507c80bae48067e957dbe07f1331c1b0c1087c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:45.062458Z","signature_b64":"4y/ErcbmstWqDPkbUTBWgLfU/5phXz7rqI18J2L651KZ4zHAyUtlpjBA8B04nZQmIDTer2YIHFNxyCYPqgWzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"806ebb1410d55587e4a91270d6507c80bae48067e957dbe07f1331c1b0c1087c","last_reissued_at":"2026-07-02T01:17:45.062041Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:45.062041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00496","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":"2026-07-02T01:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWFE6aJTmpy6fjXkMn8RSBv8zq3+5YT4uIZOOQIXofm5YiaD+LEDaenvUIOc1EBz4DroTBKBA7VIIUZzl01OCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T17:58:22.952341Z"},"content_sha256":"e2e40f8f40a57747a8f7c14a9a5757e0c84334ec7367b4cbf03f5310e6909964","schema_version":"1.0","event_id":"sha256:e2e40f8f40a57747a8f7c14a9a5757e0c84334ec7367b4cbf03f5310e6909964"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QBXLWFAQ2VKYPZFJCJYNMUD4QC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost multiplicity-one property of spherical varieties over finite fields","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fang Shi, Fulin Chen, Shaobin Tan","submitted_at":"2026-07-01T06:25:31Z","abstract_excerpt":"Let $H$ be a connected algebraic subgroup of a connected reductive group $G$ over a finite field $\\mathbb F_q$ such that $G/H$ is a $G$-spherical variety, i.e., $G/H$ has an open dense $B$-orbit for each Borel subgroup $B$ of $G$. We formulate, for the pair $(G,H)$, an almost multiplicity-one property. Then we establish a criterion for this property in terms of the $B$-stabilizers on $G/H$. In particular, we will see that this property is analogous to the strongly tempered condition in characteristic $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00496","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/2607.00496/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":"2026-07-02T01:17:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kRy0MSOb8FZI00CPLexfT+oMz5a4muyQXl6BAaOPYTo+xWCKzK63zps5aCxpv5xsU+ePnrAiXWUfFRKvHFOUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T17:58:22.952843Z"},"content_sha256":"9ac36dffe351741d52792bbf076c9723894f733b7ec7f43098020621ce877135","schema_version":"1.0","event_id":"sha256:9ac36dffe351741d52792bbf076c9723894f733b7ec7f43098020621ce877135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC/bundle.json","state_url":"https://pith.science/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC/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":"2026-08-12T17:58:22Z","links":{"resolver":"https://pith.science/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC","bundle":"https://pith.science/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC/bundle.json","state":"https://pith.science/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBXLWFAQ2VKYPZFJCJYNMUD4QC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QBXLWFAQ2VKYPZFJCJYNMUD4QC","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":"8057953b22314aa9efc8d794ef6e97358d22333f57f81581b18031bb4c1c0850","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:25:31Z","title_canon_sha256":"17138ba838fb65f10e9f6c26b433e41f5870b3b7173137442b08ea86a1111f38"},"schema_version":"1.0","source":{"id":"2607.00496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00496","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00496v1","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00496","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"QBXLWFAQ2VKY","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"QBXLWFAQ2VKYPZFJ","created_at":"2026-07-02T01:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"QBXLWFAQ","created_at":"2026-07-02T01:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:9ac36dffe351741d52792bbf076c9723894f733b7ec7f43098020621ce877135","target":"graph","created_at":"2026-07-02T01:17:45Z","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/2607.00496/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $H$ be a connected algebraic subgroup of a connected reductive group $G$ over a finite field $\\mathbb F_q$ such that $G/H$ is a $G$-spherical variety, i.e., $G/H$ has an open dense $B$-orbit for each Borel subgroup $B$ of $G$. We formulate, for the pair $(G,H)$, an almost multiplicity-one property. Then we establish a criterion for this property in terms of the $B$-stabilizers on $G/H$. In particular, we will see that this property is analogous to the strongly tempered condition in characteristic $0$.","authors_text":"Fang Shi, Fulin Chen, Shaobin Tan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:25:31Z","title":"Almost multiplicity-one property of spherical varieties over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00496","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:e2e40f8f40a57747a8f7c14a9a5757e0c84334ec7367b4cbf03f5310e6909964","target":"record","created_at":"2026-07-02T01:17:45Z","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":"8057953b22314aa9efc8d794ef6e97358d22333f57f81581b18031bb4c1c0850","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-01T06:25:31Z","title_canon_sha256":"17138ba838fb65f10e9f6c26b433e41f5870b3b7173137442b08ea86a1111f38"},"schema_version":"1.0","source":{"id":"2607.00496","kind":"arxiv","version":1}},"canonical_sha256":"806ebb1410d55587e4a91270d6507c80bae48067e957dbe07f1331c1b0c1087c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"806ebb1410d55587e4a91270d6507c80bae48067e957dbe07f1331c1b0c1087c","first_computed_at":"2026-07-02T01:17:45.062041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:45.062041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4y/ErcbmstWqDPkbUTBWgLfU/5phXz7rqI18J2L651KZ4zHAyUtlpjBA8B04nZQmIDTer2YIHFNxyCYPqgWzDg==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:45.062458Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2e40f8f40a57747a8f7c14a9a5757e0c84334ec7367b4cbf03f5310e6909964","sha256:9ac36dffe351741d52792bbf076c9723894f733b7ec7f43098020621ce877135"],"state_sha256":"5704e9c0146fc7efab3179ad5c4e5b0aa6a181537231010cf2259e5ebf9bdcbd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m/qT3awMnIDQU5onGBPlGQZGt9CV4RgJ93a5/MYpMrufihGxynCKy5T2YYL7lDkRVMRQHtRhz1So9JAwWmFsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T17:58:22.956682Z","bundle_sha256":"6219d631a17f87aa88a4b086825dda037b326785825f15a8e53a5bffc4bb1008"}}