{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EQWWPBF2R7HKSKM4CFGYIRYXQH","short_pith_number":"pith:EQWWPBF2","canonical_record":{"source":{"id":"1804.04524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-12T14:10:49Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"7090e56dfc091e19891f839f5800a64ee4af4d1db4f1cbd33be6c0f2122ec6be","abstract_canon_sha256":"363178218f937e702a707df005a62117d34d0566e475790669956e889239183a"},"schema_version":"1.0"},"canonical_sha256":"242d6784ba8fcea9299c114d84471781dfa40977148c729e5b6fde666990ea1c","source":{"kind":"arxiv","id":"1804.04524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04524","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04524v1","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04524","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"EQWWPBF2R7HK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQWWPBF2R7HKSKM4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQWWPBF2","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EQWWPBF2R7HKSKM4CFGYIRYXQH","target":"record","payload":{"canonical_record":{"source":{"id":"1804.04524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-12T14:10:49Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"7090e56dfc091e19891f839f5800a64ee4af4d1db4f1cbd33be6c0f2122ec6be","abstract_canon_sha256":"363178218f937e702a707df005a62117d34d0566e475790669956e889239183a"},"schema_version":"1.0"},"canonical_sha256":"242d6784ba8fcea9299c114d84471781dfa40977148c729e5b6fde666990ea1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:37.332870Z","signature_b64":"3zR35ElzPTiBUIMHgr3uewMxNaYPmmWHdZBoT82HVULTV5H5aimm9rUvzjCKQHwf2pUJiMzsR0G8wlzyIjaNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"242d6784ba8fcea9299c114d84471781dfa40977148c729e5b6fde666990ea1c","last_reissued_at":"2026-05-18T00:18:37.332277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:37.332277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.04524","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":"2026-05-18T00:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FW/y07G5v+3LM4msSm2IMIsbOqlaRL76hZZVPUMIYFy3rf3DmyLiRP15jDZkXgFy9puHmG5l84h2gPyOBuq+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:52:37.916278Z"},"content_sha256":"7374a1eff5da49d985ca819e5f29efca1c26432fa599871d9b4987acc62483e6","schema_version":"1.0","event_id":"sha256:7374a1eff5da49d985ca819e5f29efca1c26432fa599871d9b4987acc62483e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EQWWPBF2R7HKSKM4CFGYIRYXQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chern scalar curvature and symmetric products of compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Indranil Biswas","submitted_at":"2018-04-12T14:10:49Z","abstract_excerpt":"Let $X$ be a compact connected Riemann surface of genus $g\\geq 0$, and let ${\\rm Sym}^d(X)$, $d \\ge 1$, denote the $d$-fold symmetric product of $X$. We show that ${\\rm Sym}^d(X)$ admits a Hermitian metric with negative Chern scalar curvature if and only if $g \\geq 2$, and positive Chern scalar curvature if and only if $d > g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04524","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":""},"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":"2026-05-18T00:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZgbAid9NOHCGvPJne71fZTprN7a11ZOAaDTovUIB0BEPe4SY71f8E+ViQFrdvER2BdjZtuuLiPAy39BRzx3JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:52:37.916647Z"},"content_sha256":"5a1a8ba65283e1878395789a5430a16bbde907c4471eee117900d7e958661311","schema_version":"1.0","event_id":"sha256:5a1a8ba65283e1878395789a5430a16bbde907c4471eee117900d7e958661311"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH/bundle.json","state_url":"https://pith.science/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH/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":"2026-06-01T21:52:37Z","links":{"resolver":"https://pith.science/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH","bundle":"https://pith.science/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH/bundle.json","state":"https://pith.science/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQWWPBF2R7HKSKM4CFGYIRYXQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EQWWPBF2R7HKSKM4CFGYIRYXQH","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":"363178218f937e702a707df005a62117d34d0566e475790669956e889239183a","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-12T14:10:49Z","title_canon_sha256":"7090e56dfc091e19891f839f5800a64ee4af4d1db4f1cbd33be6c0f2122ec6be"},"schema_version":"1.0","source":{"id":"1804.04524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04524","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04524v1","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04524","created_at":"2026-05-18T00:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"EQWWPBF2R7HK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQWWPBF2R7HKSKM4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQWWPBF2","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:5a1a8ba65283e1878395789a5430a16bbde907c4471eee117900d7e958661311","target":"graph","created_at":"2026-05-18T00:18:37Z","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"},"paper":{"abstract_excerpt":"Let $X$ be a compact connected Riemann surface of genus $g\\geq 0$, and let ${\\rm Sym}^d(X)$, $d \\ge 1$, denote the $d$-fold symmetric product of $X$. We show that ${\\rm Sym}^d(X)$ admits a Hermitian metric with negative Chern scalar curvature if and only if $g \\geq 2$, and positive Chern scalar curvature if and only if $d > g$.","authors_text":"Harish Seshadri, Indranil Biswas","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-12T14:10:49Z","title":"Chern scalar curvature and symmetric products of compact Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04524","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":"sha256:7374a1eff5da49d985ca819e5f29efca1c26432fa599871d9b4987acc62483e6","target":"record","created_at":"2026-05-18T00:18:37Z","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":"363178218f937e702a707df005a62117d34d0566e475790669956e889239183a","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-12T14:10:49Z","title_canon_sha256":"7090e56dfc091e19891f839f5800a64ee4af4d1db4f1cbd33be6c0f2122ec6be"},"schema_version":"1.0","source":{"id":"1804.04524","kind":"arxiv","version":1}},"canonical_sha256":"242d6784ba8fcea9299c114d84471781dfa40977148c729e5b6fde666990ea1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"242d6784ba8fcea9299c114d84471781dfa40977148c729e5b6fde666990ea1c","first_computed_at":"2026-05-18T00:18:37.332277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:37.332277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3zR35ElzPTiBUIMHgr3uewMxNaYPmmWHdZBoT82HVULTV5H5aimm9rUvzjCKQHwf2pUJiMzsR0G8wlzyIjaNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:37.332870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.04524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7374a1eff5da49d985ca819e5f29efca1c26432fa599871d9b4987acc62483e6","sha256:5a1a8ba65283e1878395789a5430a16bbde907c4471eee117900d7e958661311"],"state_sha256":"bb66e4bc15cc0aadd2447587c7e898f3d3eb4f994576b5b9e08f485954f4886a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mUyg+RcoyXydXgXIjF+t2h26sfNefjtvjwZyY7QabZcSn5TbFq7Xf4aeSjVfQLwpEKcpI/d60gcZFKZSlmJZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:52:37.918538Z","bundle_sha256":"44ca1755820fb00c8eab46a515a358a2088a2b7b8a3cf1b8902508af8014c7f7"}}