{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:S7JDYR2UZWHJFDAANMKAUL6GZK","short_pith_number":"pith:S7JDYR2U","canonical_record":{"source":{"id":"1709.09864","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T09:21:31Z","cross_cats_sorted":[],"title_canon_sha256":"a3e22b2c4c7efefebb76290fe1bfa645b38b2bb51a0d5db943892eae009ac70a","abstract_canon_sha256":"982bf9d265aebbb953a724183d2bb735cab48e1979f4505bfb85185c7a98dd37"},"schema_version":"1.0"},"canonical_sha256":"97d23c4754cd8e928c006b140a2fc6caa4b0955b053ffbac5166b275f8659719","source":{"kind":"arxiv","id":"1709.09864","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09864","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09864v4","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09864","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"S7JDYR2UZWHJ","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"pith_short_16","alias_value":"S7JDYR2UZWHJFDAA","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"pith_short_8","alias_value":"S7JDYR2U","created_at":"2026-07-05T01:07:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:S7JDYR2UZWHJFDAANMKAUL6GZK","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09864","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T09:21:31Z","cross_cats_sorted":[],"title_canon_sha256":"a3e22b2c4c7efefebb76290fe1bfa645b38b2bb51a0d5db943892eae009ac70a","abstract_canon_sha256":"982bf9d265aebbb953a724183d2bb735cab48e1979f4505bfb85185c7a98dd37"},"schema_version":"1.0"},"canonical_sha256":"97d23c4754cd8e928c006b140a2fc6caa4b0955b053ffbac5166b275f8659719","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:34.941369Z","signature_b64":"RL5ZOzS+Fr0x1V/wVj8shAjGrj4XXdlyxh1RGGGThthF/LjU3p1IQ0+Ib3uese184CWiWbmgjev7FC620JOmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97d23c4754cd8e928c006b140a2fc6caa4b0955b053ffbac5166b275f8659719","last_reissued_at":"2026-07-05T01:07:34.940862Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:34.940862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09864","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YnTfMmc2ncn9S8YMJyBPi5xqg8qVu0XE1g8Cig2THv23UBRKll/APQr+mavUF7w7Sp3jwtn+Z6wd8e7D2cZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T03:07:48.557971Z"},"content_sha256":"96c35dbd5e483ca393af66e72847b9f6c275a99f299b254eb307ea3cc1e3676a","schema_version":"1.0","event_id":"sha256:96c35dbd5e483ca393af66e72847b9f6c275a99f299b254eb307ea3cc1e3676a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:S7JDYR2UZWHJFDAANMKAUL6GZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decomposition of degenerate Gromov-Witten invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bernd Siebert, Dan Abramovich, Mark Gross, Qile Chen","submitted_at":"2017-09-28T09:21:31Z","abstract_excerpt":"We prove a decomposition formula of logarithmic Gromov-Witten invariants in a degeneration setting. A one-parameter log smooth family X->B with singular fibre over b_0 \\in B yields a family M(X/B,\\beta) -> B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b_0 in terms of rigid tropical curves. This generalizes one aspect of known results in the case that the fibre X_{b_0} is a normal crossings union of two divisors. We exhibit our formulas in explicit examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09864","kind":"arxiv","version":4},"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/1709.09864/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":"2026-07-05T01:07:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRPuz92ZukeqCFdqAaeX0HiOtHUemEexmh1+0A1G7ybQHNO8dvAavqTlvox1suvTZcf2e0JEHFu2yAkA2tZqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T03:07:48.558354Z"},"content_sha256":"e72ddb65990c64a5be49bfde72b892b205ee12ab70e2127485f78e95fb32b103","schema_version":"1.0","event_id":"sha256:e72ddb65990c64a5be49bfde72b892b205ee12ab70e2127485f78e95fb32b103"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7JDYR2UZWHJFDAANMKAUL6GZK/bundle.json","state_url":"https://pith.science/pith/S7JDYR2UZWHJFDAANMKAUL6GZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7JDYR2UZWHJFDAANMKAUL6GZK/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":"2026-07-19T03:07:48Z","links":{"resolver":"https://pith.science/pith/S7JDYR2UZWHJFDAANMKAUL6GZK","bundle":"https://pith.science/pith/S7JDYR2UZWHJFDAANMKAUL6GZK/bundle.json","state":"https://pith.science/pith/S7JDYR2UZWHJFDAANMKAUL6GZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7JDYR2UZWHJFDAANMKAUL6GZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S7JDYR2UZWHJFDAANMKAUL6GZK","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":"982bf9d265aebbb953a724183d2bb735cab48e1979f4505bfb85185c7a98dd37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T09:21:31Z","title_canon_sha256":"a3e22b2c4c7efefebb76290fe1bfa645b38b2bb51a0d5db943892eae009ac70a"},"schema_version":"1.0","source":{"id":"1709.09864","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09864","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09864v4","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09864","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"pith_short_12","alias_value":"S7JDYR2UZWHJ","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"pith_short_16","alias_value":"S7JDYR2UZWHJFDAA","created_at":"2026-07-05T01:07:34Z"},{"alias_kind":"pith_short_8","alias_value":"S7JDYR2U","created_at":"2026-07-05T01:07:34Z"}],"graph_snapshots":[{"event_id":"sha256:e72ddb65990c64a5be49bfde72b892b205ee12ab70e2127485f78e95fb32b103","target":"graph","created_at":"2026-07-05T01:07:34Z","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/1709.09864/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a decomposition formula of logarithmic Gromov-Witten invariants in a degeneration setting. A one-parameter log smooth family X->B with singular fibre over b_0 \\in B yields a family M(X/B,\\beta) -> B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b_0 in terms of rigid tropical curves. This generalizes one aspect of known results in the case that the fibre X_{b_0} is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.","authors_text":"Bernd Siebert, Dan Abramovich, Mark Gross, Qile Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T09:21:31Z","title":"Decomposition of degenerate Gromov-Witten invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09864","kind":"arxiv","version":4},"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":"sha256:96c35dbd5e483ca393af66e72847b9f6c275a99f299b254eb307ea3cc1e3676a","target":"record","created_at":"2026-07-05T01:07:34Z","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":"982bf9d265aebbb953a724183d2bb735cab48e1979f4505bfb85185c7a98dd37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-28T09:21:31Z","title_canon_sha256":"a3e22b2c4c7efefebb76290fe1bfa645b38b2bb51a0d5db943892eae009ac70a"},"schema_version":"1.0","source":{"id":"1709.09864","kind":"arxiv","version":4}},"canonical_sha256":"97d23c4754cd8e928c006b140a2fc6caa4b0955b053ffbac5166b275f8659719","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97d23c4754cd8e928c006b140a2fc6caa4b0955b053ffbac5166b275f8659719","first_computed_at":"2026-07-05T01:07:34.940862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:07:34.940862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RL5ZOzS+Fr0x1V/wVj8shAjGrj4XXdlyxh1RGGGThthF/LjU3p1IQ0+Ib3uese184CWiWbmgjev7FC620JOmAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:07:34.941369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09864","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96c35dbd5e483ca393af66e72847b9f6c275a99f299b254eb307ea3cc1e3676a","sha256:e72ddb65990c64a5be49bfde72b892b205ee12ab70e2127485f78e95fb32b103"],"state_sha256":"18da11a050389c8d6478f29a6397571d504a6e79238dca587f1e986865549786"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7AjQMSWZXLhaxRby/YrfGe6nyWBU7reeSPGzUE3T7zpQlrSLMy0HawxwmaVUP7ol+iZyNOz+4xBG1pDe1acBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-19T03:07:48.560508Z","bundle_sha256":"1f8fb0aef0cec5c20e9e31cfe6444b0defbe4a1f8a45cb16d53b1d3c106e9848"}}