{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G7E77O7VX6P3NB5CWIFTRWGO3E","short_pith_number":"pith:G7E77O7V","canonical_record":{"source":{"id":"1301.4409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-18T15:52:07Z","cross_cats_sorted":["math.AT","math.CV"],"title_canon_sha256":"1d0f3855207dcb5712f3702ccc11e433720224f05d89144ad60470173b310c03","abstract_canon_sha256":"e91c754d5dc025f55c51c895207de3124feb2748347d487f6577f23982d8524d"},"schema_version":"1.0"},"canonical_sha256":"37c9ffbbf5bf9fb687a2b20b38d8ced91393016a8a823f832f2e4b07c5c870fe","source":{"kind":"arxiv","id":"1301.4409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4409","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4409v1","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4409","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"G7E77O7VX6P3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G7E77O7VX6P3NB5C","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G7E77O7V","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G7E77O7VX6P3NB5CWIFTRWGO3E","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-18T15:52:07Z","cross_cats_sorted":["math.AT","math.CV"],"title_canon_sha256":"1d0f3855207dcb5712f3702ccc11e433720224f05d89144ad60470173b310c03","abstract_canon_sha256":"e91c754d5dc025f55c51c895207de3124feb2748347d487f6577f23982d8524d"},"schema_version":"1.0"},"canonical_sha256":"37c9ffbbf5bf9fb687a2b20b38d8ced91393016a8a823f832f2e4b07c5c870fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:05.471050Z","signature_b64":"Ir4nH6b9Rz+fT9LdU9exmXOqkHuf79xqo2u/qDuWAKsMM53LYiy2w0pKBeN5UmG5m8f6Offg5gAEFvu6523CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37c9ffbbf5bf9fb687a2b20b38d8ced91393016a8a823f832f2e4b07c5c870fe","last_reissued_at":"2026-05-18T03:36:05.470590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:05.470590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4409","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":"2026-05-18T03:36:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7mSs3NRnw+gblnaAA+old9W2syGRiIaN8CYoBOSwy1gV5AlT0TWsQ9LdvaV5/ULXt6CyiyeziChjOr4/JhuGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:08:26.251263Z"},"content_sha256":"8d3684bf58f63c5d0f513fdf910aeaff7df07be5cba0338184a9eb8fee1c69bb","schema_version":"1.0","event_id":"sha256:8d3684bf58f63c5d0f513fdf910aeaff7df07be5cba0338184a9eb8fee1c69bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G7E77O7VX6P3NB5CWIFTRWGO3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Genus stabilization for moduli of curves with symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CV"],"primary_cat":"math.AG","authors_text":"Fabio Perroni (SISSA-Trieste), Fabrizio Catanese (Bayreuth), Michael L\\\"onne (Hannover)","submitted_at":"2013-01-18T15:52:07Z","abstract_excerpt":"In a previous paper, arXiv:1206.5498, we introduced a new homological invariant $\\e$ for the faithful action of a finite group G on an algebraic curve.\n  We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant $\\e$, if the genus g' of the quotient curve is sufficiently large, is irreducible (and non empty iff the class satisfies the condition which we define as 'admissibility'). In the unramified case, a similar result had been proven by Dunfield and Thurston using the classical invariant in the second homology group of G,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4409","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":"2026-05-18T03:36:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5b2f6O1UhejZpdQZ5At3xP+AuqchMHm1Y315TWxMBeKJHWKpHJqTEO/oDx02kZvJ8kWZmPCiEKINJ3PEjcpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:08:26.251626Z"},"content_sha256":"3b658860bb967acd06dfc739d98083f2f1cd844873a3f1e7d5a78b4f78c3fbc8","schema_version":"1.0","event_id":"sha256:3b658860bb967acd06dfc739d98083f2f1cd844873a3f1e7d5a78b4f78c3fbc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7E77O7VX6P3NB5CWIFTRWGO3E/bundle.json","state_url":"https://pith.science/pith/G7E77O7VX6P3NB5CWIFTRWGO3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7E77O7VX6P3NB5CWIFTRWGO3E/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":"2026-06-26T07:08:26Z","links":{"resolver":"https://pith.science/pith/G7E77O7VX6P3NB5CWIFTRWGO3E","bundle":"https://pith.science/pith/G7E77O7VX6P3NB5CWIFTRWGO3E/bundle.json","state":"https://pith.science/pith/G7E77O7VX6P3NB5CWIFTRWGO3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7E77O7VX6P3NB5CWIFTRWGO3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G7E77O7VX6P3NB5CWIFTRWGO3E","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":"e91c754d5dc025f55c51c895207de3124feb2748347d487f6577f23982d8524d","cross_cats_sorted":["math.AT","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-18T15:52:07Z","title_canon_sha256":"1d0f3855207dcb5712f3702ccc11e433720224f05d89144ad60470173b310c03"},"schema_version":"1.0","source":{"id":"1301.4409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4409","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4409v1","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4409","created_at":"2026-05-18T03:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"G7E77O7VX6P3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G7E77O7VX6P3NB5C","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G7E77O7V","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:3b658860bb967acd06dfc739d98083f2f1cd844873a3f1e7d5a78b4f78c3fbc8","target":"graph","created_at":"2026-05-18T03:36:05Z","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":"In a previous paper, arXiv:1206.5498, we introduced a new homological invariant $\\e$ for the faithful action of a finite group G on an algebraic curve.\n  We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant $\\e$, if the genus g' of the quotient curve is sufficiently large, is irreducible (and non empty iff the class satisfies the condition which we define as 'admissibility'). In the unramified case, a similar result had been proven by Dunfield and Thurston using the classical invariant in the second homology group of G,","authors_text":"Fabio Perroni (SISSA-Trieste), Fabrizio Catanese (Bayreuth), Michael L\\\"onne (Hannover)","cross_cats":["math.AT","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-18T15:52:07Z","title":"Genus stabilization for moduli of curves with symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4409","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":"sha256:8d3684bf58f63c5d0f513fdf910aeaff7df07be5cba0338184a9eb8fee1c69bb","target":"record","created_at":"2026-05-18T03:36:05Z","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":"e91c754d5dc025f55c51c895207de3124feb2748347d487f6577f23982d8524d","cross_cats_sorted":["math.AT","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-18T15:52:07Z","title_canon_sha256":"1d0f3855207dcb5712f3702ccc11e433720224f05d89144ad60470173b310c03"},"schema_version":"1.0","source":{"id":"1301.4409","kind":"arxiv","version":1}},"canonical_sha256":"37c9ffbbf5bf9fb687a2b20b38d8ced91393016a8a823f832f2e4b07c5c870fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37c9ffbbf5bf9fb687a2b20b38d8ced91393016a8a823f832f2e4b07c5c870fe","first_computed_at":"2026-05-18T03:36:05.470590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:05.470590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ir4nH6b9Rz+fT9LdU9exmXOqkHuf79xqo2u/qDuWAKsMM53LYiy2w0pKBeN5UmG5m8f6Offg5gAEFvu6523CDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:05.471050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d3684bf58f63c5d0f513fdf910aeaff7df07be5cba0338184a9eb8fee1c69bb","sha256:3b658860bb967acd06dfc739d98083f2f1cd844873a3f1e7d5a78b4f78c3fbc8"],"state_sha256":"58c5701bc31ef22318cdbd3fd9129191b463ea1356da086107740e21a0f47141"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXKbavAXUr3pCVW2T2y4FaNV9SBhq6N/rfkTBu07G8wz7pOUv4KGwKY7q7g1bFeGNf2EzjVMi8ICE5pgWQkNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:08:26.253863Z","bundle_sha256":"5e4cb15c83b18f66ef0bbfa00f007c4346dc197022f3c722e4633609880078b3"}}