{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LZQCNUZAGHKMVSNBLCR3MASWF5","short_pith_number":"pith:LZQCNUZA","canonical_record":{"source":{"id":"2606.27362","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T17:58:26Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ae753b12060a125357545fe53c395607d02b79b5a43027c8028c62c32d83ae29","abstract_canon_sha256":"911c120fbba86896f860092b5315e1c3391696cb7fe8afb4b1a4401cf0d93c81"},"schema_version":"1.0"},"canonical_sha256":"5e6026d32031d4cac9a158a3b602562f4ce6178d55c2d5938cd7119a1c1f6404","source":{"kind":"arxiv","id":"2606.27362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27362","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27362v1","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27362","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"LZQCNUZAGHKM","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_16","alias_value":"LZQCNUZAGHKMVSNB","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_8","alias_value":"LZQCNUZA","created_at":"2026-06-26T01:16:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LZQCNUZAGHKMVSNBLCR3MASWF5","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27362","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T17:58:26Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ae753b12060a125357545fe53c395607d02b79b5a43027c8028c62c32d83ae29","abstract_canon_sha256":"911c120fbba86896f860092b5315e1c3391696cb7fe8afb4b1a4401cf0d93c81"},"schema_version":"1.0"},"canonical_sha256":"5e6026d32031d4cac9a158a3b602562f4ce6178d55c2d5938cd7119a1c1f6404","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:19.824566Z","signature_b64":"QJRBYYhwJBU9xT4/fMqDTc5vwEaALsyWtYMNar+H7n1oai3D34cRewRq76OPO1nBsa2fDz8BPoBT13NWbui8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e6026d32031d4cac9a158a3b602562f4ce6178d55c2d5938cd7119a1c1f6404","last_reissued_at":"2026-06-26T01:16:19.824044Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:19.824044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27362","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":"2026-06-26T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Az+JTHUhXF9lfgzte1gV7mxBlEqtyTbh8FZ7Ks1PZbFvE4iZB9khyfcePkWqkVShjVmmfXAUtd+9xDoW8KfHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:58:01.760178Z"},"content_sha256":"e42c693628ae088807fb453ec5a594cecbe1626e614cc25b6cbc446d5aee1d47","schema_version":"1.0","event_id":"sha256:e42c693628ae088807fb453ec5a594cecbe1626e614cc25b6cbc446d5aee1d47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LZQCNUZAGHKMVSNBLCR3MASWF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hall Geometry and Auslander-Reiten Quiver","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Aayush Verma","submitted_at":"2026-06-25T17:58:26Z","abstract_excerpt":"We show how the geometric information in the motivic Hall algebra and the correspondence of the moduli stack recovers the Auslander-Reiten sequences and the Auslander-Reiten quiver."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27362","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/2606.27362/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":"2026-06-26T01:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3VjGRKrNl84p7xfxply9QoICUoL3tB1oGGrltdohfj9PzDRt6Cu2MIx3jWyuc1vbbxPE7Jl9TRE6lgJmNGZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:58:01.760554Z"},"content_sha256":"b5c63814dc512bc22818cdf4d17cfac4330af34609297c1b06a1c67a0a63e70a","schema_version":"1.0","event_id":"sha256:b5c63814dc512bc22818cdf4d17cfac4330af34609297c1b06a1c67a0a63e70a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZQCNUZAGHKMVSNBLCR3MASWF5/bundle.json","state_url":"https://pith.science/pith/LZQCNUZAGHKMVSNBLCR3MASWF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZQCNUZAGHKMVSNBLCR3MASWF5/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":"2026-07-03T10:58:01Z","links":{"resolver":"https://pith.science/pith/LZQCNUZAGHKMVSNBLCR3MASWF5","bundle":"https://pith.science/pith/LZQCNUZAGHKMVSNBLCR3MASWF5/bundle.json","state":"https://pith.science/pith/LZQCNUZAGHKMVSNBLCR3MASWF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZQCNUZAGHKMVSNBLCR3MASWF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LZQCNUZAGHKMVSNBLCR3MASWF5","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":"911c120fbba86896f860092b5315e1c3391696cb7fe8afb4b1a4401cf0d93c81","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T17:58:26Z","title_canon_sha256":"ae753b12060a125357545fe53c395607d02b79b5a43027c8028c62c32d83ae29"},"schema_version":"1.0","source":{"id":"2606.27362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27362","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27362v1","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27362","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"LZQCNUZAGHKM","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_16","alias_value":"LZQCNUZAGHKMVSNB","created_at":"2026-06-26T01:16:19Z"},{"alias_kind":"pith_short_8","alias_value":"LZQCNUZA","created_at":"2026-06-26T01:16:19Z"}],"graph_snapshots":[{"event_id":"sha256:b5c63814dc512bc22818cdf4d17cfac4330af34609297c1b06a1c67a0a63e70a","target":"graph","created_at":"2026-06-26T01:16:19Z","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/2606.27362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show how the geometric information in the motivic Hall algebra and the correspondence of the moduli stack recovers the Auslander-Reiten sequences and the Auslander-Reiten quiver.","authors_text":"Aayush Verma","cross_cats":["math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T17:58:26Z","title":"Hall Geometry and Auslander-Reiten Quiver"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27362","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:e42c693628ae088807fb453ec5a594cecbe1626e614cc25b6cbc446d5aee1d47","target":"record","created_at":"2026-06-26T01:16:19Z","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":"911c120fbba86896f860092b5315e1c3391696cb7fe8afb4b1a4401cf0d93c81","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-25T17:58:26Z","title_canon_sha256":"ae753b12060a125357545fe53c395607d02b79b5a43027c8028c62c32d83ae29"},"schema_version":"1.0","source":{"id":"2606.27362","kind":"arxiv","version":1}},"canonical_sha256":"5e6026d32031d4cac9a158a3b602562f4ce6178d55c2d5938cd7119a1c1f6404","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e6026d32031d4cac9a158a3b602562f4ce6178d55c2d5938cd7119a1c1f6404","first_computed_at":"2026-06-26T01:16:19.824044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:19.824044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QJRBYYhwJBU9xT4/fMqDTc5vwEaALsyWtYMNar+H7n1oai3D34cRewRq76OPO1nBsa2fDz8BPoBT13NWbui8AQ==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:19.824566Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e42c693628ae088807fb453ec5a594cecbe1626e614cc25b6cbc446d5aee1d47","sha256:b5c63814dc512bc22818cdf4d17cfac4330af34609297c1b06a1c67a0a63e70a"],"state_sha256":"58aeae3a90aaca2d3e2de716cc2a2e2136c679916fea4f1f6dcbb175498238c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Ra4o+rD0GHLovJBDQbj5KTGG5KxzxtZYuzAY6kTj8Fw7Fb8GIy4Ikb1h8d4e/V60W3BNRmGE3z4JtJcpM00BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T10:58:01.762647Z","bundle_sha256":"3e90bfc756c4c581f99b314e059425b3fde1068e22d7cba38097690d1a303c34"}}