{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:I4MSOI7V6GROWE6UUJVEENFRQ2","short_pith_number":"pith:I4MSOI7V","canonical_record":{"source":{"id":"2112.07504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-12-14T16:08:29Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"f992aa89e77b6db9c9e66601fdfc1566b33fc4c8ab947136e5fb58eeea369d9a","abstract_canon_sha256":"1c2bf2f96158c06c7c1683f93b8defe91386b14014d50e2ddbb1c76734b355ba"},"schema_version":"1.0"},"canonical_sha256":"47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43","source":{"kind":"arxiv","id":"2112.07504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.07504","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"arxiv_version","alias_value":"2112.07504v2","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.07504","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"pith_short_12","alias_value":"I4MSOI7V6GRO","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"pith_short_16","alias_value":"I4MSOI7V6GROWE6U","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"pith_short_8","alias_value":"I4MSOI7V","created_at":"2026-07-05T04:48:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:I4MSOI7V6GROWE6UUJVEENFRQ2","target":"record","payload":{"canonical_record":{"source":{"id":"2112.07504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-12-14T16:08:29Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"f992aa89e77b6db9c9e66601fdfc1566b33fc4c8ab947136e5fb58eeea369d9a","abstract_canon_sha256":"1c2bf2f96158c06c7c1683f93b8defe91386b14014d50e2ddbb1c76734b355ba"},"schema_version":"1.0"},"canonical_sha256":"47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:48:39.774622Z","signature_b64":"A66aaucvcc40ukqjs1Ievebok8Qg0pqQV80VQObFozlFG4yjNUEpQUqej4D0tV5QfX0aNlwjuF3nRCg+EvUAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43","last_reissued_at":"2026-07-05T04:48:39.774233Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:48:39.774233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.07504","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":"2026-07-05T04:48:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LZeXMOD7ECDPZSiSUdDPnTMrkmKBKamMAZwbZlu5Vhb/eYZVrxGpNzvcfTxNgGrT87sH4To/CbysZ2S6qqDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:50:32.118707Z"},"content_sha256":"5ce9268e2419706c957695fddc5b2b6be329f1ed31e9be4c81eac4acbcc941c2","schema_version":"1.0","event_id":"sha256:5ce9268e2419706c957695fddc5b2b6be329f1ed31e9be4c81eac4acbcc941c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:I4MSOI7V6GROWE6UUJVEENFRQ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Torelli-type theorems for gravitational instantons with quadratic volume growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.DG","authors_text":"Gao Chen, Jeff Viaclovsky, Ruobing Zhang","submitted_at":"2021-12-14T16:08:29Z","abstract_excerpt":"We prove Torelli-type uniqueness theorems for both ALG$^*$ gravitational instantons and ALG gravitational instantons which are of order $2$. That is, the periods uniquely characterize these types of gravitational instantons up to diffeomorphism. We define a period mapping $\\mathscr{P}$, which we show is surjective in the ALG cases, and open in the ALG$^*$ cases. We also construct some new degenerations of hyperk\\\"ahler metrics on the K3 surface which exhibit bubbling of ALG$^*$ gravitational instantons."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.07504","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/2112.07504/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":"2026-07-05T04:48:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/izg98tZxHaDIJqfRsLgfribRmtYKPTgqWFhFlcxmq8NfhODv31NZ/LCl7L2N2Qm8aTHntxDjeSdUP22i4goCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:50:32.119098Z"},"content_sha256":"3d091be51d72c03d734dc72fd8410b0ea8ce373f0e00b675d74564e67b4d9164","schema_version":"1.0","event_id":"sha256:3d091be51d72c03d734dc72fd8410b0ea8ce373f0e00b675d74564e67b4d9164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4MSOI7V6GROWE6UUJVEENFRQ2/bundle.json","state_url":"https://pith.science/pith/I4MSOI7V6GROWE6UUJVEENFRQ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4MSOI7V6GROWE6UUJVEENFRQ2/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":"2026-08-05T02:50:32Z","links":{"resolver":"https://pith.science/pith/I4MSOI7V6GROWE6UUJVEENFRQ2","bundle":"https://pith.science/pith/I4MSOI7V6GROWE6UUJVEENFRQ2/bundle.json","state":"https://pith.science/pith/I4MSOI7V6GROWE6UUJVEENFRQ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4MSOI7V6GROWE6UUJVEENFRQ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:I4MSOI7V6GROWE6UUJVEENFRQ2","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":"1c2bf2f96158c06c7c1683f93b8defe91386b14014d50e2ddbb1c76734b355ba","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-12-14T16:08:29Z","title_canon_sha256":"f992aa89e77b6db9c9e66601fdfc1566b33fc4c8ab947136e5fb58eeea369d9a"},"schema_version":"1.0","source":{"id":"2112.07504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.07504","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"arxiv_version","alias_value":"2112.07504v2","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.07504","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"pith_short_12","alias_value":"I4MSOI7V6GRO","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"pith_short_16","alias_value":"I4MSOI7V6GROWE6U","created_at":"2026-07-05T04:48:39Z"},{"alias_kind":"pith_short_8","alias_value":"I4MSOI7V","created_at":"2026-07-05T04:48:39Z"}],"graph_snapshots":[{"event_id":"sha256:3d091be51d72c03d734dc72fd8410b0ea8ce373f0e00b675d74564e67b4d9164","target":"graph","created_at":"2026-07-05T04:48:39Z","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/2112.07504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove Torelli-type uniqueness theorems for both ALG$^*$ gravitational instantons and ALG gravitational instantons which are of order $2$. That is, the periods uniquely characterize these types of gravitational instantons up to diffeomorphism. We define a period mapping $\\mathscr{P}$, which we show is surjective in the ALG cases, and open in the ALG$^*$ cases. We also construct some new degenerations of hyperk\\\"ahler metrics on the K3 surface which exhibit bubbling of ALG$^*$ gravitational instantons.","authors_text":"Gao Chen, Jeff Viaclovsky, Ruobing Zhang","cross_cats":["math-ph","math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-12-14T16:08:29Z","title":"Torelli-type theorems for gravitational instantons with quadratic volume growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.07504","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":"sha256:5ce9268e2419706c957695fddc5b2b6be329f1ed31e9be4c81eac4acbcc941c2","target":"record","created_at":"2026-07-05T04:48:39Z","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":"1c2bf2f96158c06c7c1683f93b8defe91386b14014d50e2ddbb1c76734b355ba","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-12-14T16:08:29Z","title_canon_sha256":"f992aa89e77b6db9c9e66601fdfc1566b33fc4c8ab947136e5fb58eeea369d9a"},"schema_version":"1.0","source":{"id":"2112.07504","kind":"arxiv","version":2}},"canonical_sha256":"47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47192723f5f1a2eb13d4a26a4234b186b008c582cb924411e48d87d73195fc43","first_computed_at":"2026-07-05T04:48:39.774233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:48:39.774233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A66aaucvcc40ukqjs1Ievebok8Qg0pqQV80VQObFozlFG4yjNUEpQUqej4D0tV5QfX0aNlwjuF3nRCg+EvUAAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:48:39.774622Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.07504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ce9268e2419706c957695fddc5b2b6be329f1ed31e9be4c81eac4acbcc941c2","sha256:3d091be51d72c03d734dc72fd8410b0ea8ce373f0e00b675d74564e67b4d9164"],"state_sha256":"7c969ca2b7ef201c745d2d3707aeaa1b8fc70023eb8356d7e014707abd1fcec0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzJcilk9XKNbIHqClUYHdwcyqYwOxkdZ9wPMjAAl8LJE9efN6CTYtcnKUmKY0QTcaBx26BqePcYfrrqYLqhEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:50:32.121605Z","bundle_sha256":"5aeb5651e7fddadd7637ad71f3a31348afe5a53bb3cb7e464a68d133e02e1c08"}}