{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LGJZPG3NO24IA4OHB7NB256ZPQ","short_pith_number":"pith:LGJZPG3N","canonical_record":{"source":{"id":"2502.04608","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-07T01:49:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"c19706e143cd1f3eff5fa2fed1a54763bf58393b8adb938dd77f9f2da6a17eec","abstract_canon_sha256":"4e38ab7dda869d02458f9df5c9c126f74a16cc903cf7cbffaa209e4f6d9de478"},"schema_version":"1.0"},"canonical_sha256":"5993979b6d76b88071c70fda1d77d97c201bd326698a18b82bdca122b88e6a27","source":{"kind":"arxiv","id":"2502.04608","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04608","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04608v2","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04608","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"pith_short_12","alias_value":"LGJZPG3NO24I","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"pith_short_16","alias_value":"LGJZPG3NO24IA4OH","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"pith_short_8","alias_value":"LGJZPG3N","created_at":"2026-06-23T02:13:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LGJZPG3NO24IA4OHB7NB256ZPQ","target":"record","payload":{"canonical_record":{"source":{"id":"2502.04608","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-07T01:49:51Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"c19706e143cd1f3eff5fa2fed1a54763bf58393b8adb938dd77f9f2da6a17eec","abstract_canon_sha256":"4e38ab7dda869d02458f9df5c9c126f74a16cc903cf7cbffaa209e4f6d9de478"},"schema_version":"1.0"},"canonical_sha256":"5993979b6d76b88071c70fda1d77d97c201bd326698a18b82bdca122b88e6a27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:13.912020Z","signature_b64":"OjgyrYqmwwvZH9m0HTjzwxbuUjl7ITc7Dq6LEHSXkXVoqgAfaDPpwSmlofLMtYEr4WCyTxHzOVT6u5BZ0wNiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5993979b6d76b88071c70fda1d77d97c201bd326698a18b82bdca122b88e6a27","last_reissued_at":"2026-06-23T02:13:13.911563Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:13.911563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.04608","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":"2026-06-23T02:13:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J3PZu32edm9zuKTUoqZ9gXJBkEF31a6JmH8N2XyOKN3D2Y24dm6PdT5Yiizui/YbJ5JMLhRHWW8Z9qjKDOamDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:03:28.673336Z"},"content_sha256":"c97e50b4b20b5a122f50c3049664475464a5f598ca4fcece9d32ec5a3cf4db89","schema_version":"1.0","event_id":"sha256:c97e50b4b20b5a122f50c3049664475464a5f598ca4fcece9d32ec5a3cf4db89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LGJZPG3NO24IA4OHB7NB256ZPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic cycles and values of Green's functions -- Products of Elliptic Curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ramesh Sreekantan (with an appendix by Kannappan Sampath)","submitted_at":"2025-02-07T01:49:51Z","abstract_excerpt":"Gross and Zagier defined certain `higher Green's functions' on products of modular curves and conjectured that the value of these functions at complex multiplication points should be logarithms of algebraic numbers. This is now a theorem of Li and Bruinier-Li-Yang. We relate this conjecture to the existence of motivic cycles in the universal family of products of elliptic curves along the lines of Mellit and Zhang. Using this we are able to prove Zagier's conjecture in some cases when the two CM points have the same discriminant. This is originally a theorem of Viazovska. Li, Bruinier-Li-Yang,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04608","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.04608/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":"2026-06-23T02:13:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0SaB1uf9m0ER9LMkPqzxSXI5TDRhclenVj1SrRybZPgGsm/9DBKjvl1l0n8vF+cNfR1XymN12Ffdfd11GH9MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:03:28.673842Z"},"content_sha256":"0617b7688bace9afbb93a36eacfe92ac0912bde40933598a830f022a6385b980","schema_version":"1.0","event_id":"sha256:0617b7688bace9afbb93a36eacfe92ac0912bde40933598a830f022a6385b980"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGJZPG3NO24IA4OHB7NB256ZPQ/bundle.json","state_url":"https://pith.science/pith/LGJZPG3NO24IA4OHB7NB256ZPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGJZPG3NO24IA4OHB7NB256ZPQ/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":"2026-08-09T04:03:28Z","links":{"resolver":"https://pith.science/pith/LGJZPG3NO24IA4OHB7NB256ZPQ","bundle":"https://pith.science/pith/LGJZPG3NO24IA4OHB7NB256ZPQ/bundle.json","state":"https://pith.science/pith/LGJZPG3NO24IA4OHB7NB256ZPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGJZPG3NO24IA4OHB7NB256ZPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LGJZPG3NO24IA4OHB7NB256ZPQ","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":"4e38ab7dda869d02458f9df5c9c126f74a16cc903cf7cbffaa209e4f6d9de478","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-07T01:49:51Z","title_canon_sha256":"c19706e143cd1f3eff5fa2fed1a54763bf58393b8adb938dd77f9f2da6a17eec"},"schema_version":"1.0","source":{"id":"2502.04608","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04608","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04608v2","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04608","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"pith_short_12","alias_value":"LGJZPG3NO24I","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"pith_short_16","alias_value":"LGJZPG3NO24IA4OH","created_at":"2026-06-23T02:13:13Z"},{"alias_kind":"pith_short_8","alias_value":"LGJZPG3N","created_at":"2026-06-23T02:13:13Z"}],"graph_snapshots":[{"event_id":"sha256:0617b7688bace9afbb93a36eacfe92ac0912bde40933598a830f022a6385b980","target":"graph","created_at":"2026-06-23T02:13:13Z","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/2502.04608/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gross and Zagier defined certain `higher Green's functions' on products of modular curves and conjectured that the value of these functions at complex multiplication points should be logarithms of algebraic numbers. This is now a theorem of Li and Bruinier-Li-Yang. We relate this conjecture to the existence of motivic cycles in the universal family of products of elliptic curves along the lines of Mellit and Zhang. Using this we are able to prove Zagier's conjecture in some cases when the two CM points have the same discriminant. This is originally a theorem of Viazovska. Li, Bruinier-Li-Yang,","authors_text":"Ramesh Sreekantan (with an appendix by Kannappan Sampath)","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-07T01:49:51Z","title":"Algebraic cycles and values of Green's functions -- Products of Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04608","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:c97e50b4b20b5a122f50c3049664475464a5f598ca4fcece9d32ec5a3cf4db89","target":"record","created_at":"2026-06-23T02:13:13Z","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":"4e38ab7dda869d02458f9df5c9c126f74a16cc903cf7cbffaa209e4f6d9de478","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-07T01:49:51Z","title_canon_sha256":"c19706e143cd1f3eff5fa2fed1a54763bf58393b8adb938dd77f9f2da6a17eec"},"schema_version":"1.0","source":{"id":"2502.04608","kind":"arxiv","version":2}},"canonical_sha256":"5993979b6d76b88071c70fda1d77d97c201bd326698a18b82bdca122b88e6a27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5993979b6d76b88071c70fda1d77d97c201bd326698a18b82bdca122b88e6a27","first_computed_at":"2026-06-23T02:13:13.911563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:13.911563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OjgyrYqmwwvZH9m0HTjzwxbuUjl7ITc7Dq6LEHSXkXVoqgAfaDPpwSmlofLMtYEr4WCyTxHzOVT6u5BZ0wNiDw==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:13.912020Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.04608","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c97e50b4b20b5a122f50c3049664475464a5f598ca4fcece9d32ec5a3cf4db89","sha256:0617b7688bace9afbb93a36eacfe92ac0912bde40933598a830f022a6385b980"],"state_sha256":"72f4cd737afc48f83eaf2b9c858186dc73f0d97153053abf6f5bc540b6075166"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRk8jrsilgEsW99OBy1TY5HUv8NBqZDju8YRgsQT4da4JC8aEupTxekckCegQs0xvTnc4pB+GrSgxvTXuXffBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:03:28.677064Z","bundle_sha256":"ef01e30c7439904187be7c40e19d7222ec07602620c5614bddd9753ffc253139"}}