{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:YD52LAIVVNONKA5F3572WIYWT2","short_pith_number":"pith:YD52LAIV","canonical_record":{"source":{"id":"dg-ga/9701011","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1997-01-27T22:46:22Z","cross_cats_sorted":["alg-geom","math.AG","math.DG"],"title_canon_sha256":"84d5a0c27075cada7a66e39070b6b7dd326fcafd58be77bb4793f05b98bcb3df","abstract_canon_sha256":"60176392e2dc92a2038de91195d5415a20512b54dd3f3eb0cea3a7349ae2dacb"},"schema_version":"1.0"},"canonical_sha256":"c0fba58115ab5cd503a5df7fab23169ebbfc150ab1ff7590303dd07f464c7f84","source":{"kind":"arxiv","id":"dg-ga/9701011","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9701011","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9701011v2","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9701011","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"YD52LAIVVNON","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"pith_short_16","alias_value":"YD52LAIVVNONKA5F","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"pith_short_8","alias_value":"YD52LAIV","created_at":"2026-07-04T15:07:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:YD52LAIVVNONKA5F3572WIYWT2","target":"record","payload":{"canonical_record":{"source":{"id":"dg-ga/9701011","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1997-01-27T22:46:22Z","cross_cats_sorted":["alg-geom","math.AG","math.DG"],"title_canon_sha256":"84d5a0c27075cada7a66e39070b6b7dd326fcafd58be77bb4793f05b98bcb3df","abstract_canon_sha256":"60176392e2dc92a2038de91195d5415a20512b54dd3f3eb0cea3a7349ae2dacb"},"schema_version":"1.0"},"canonical_sha256":"c0fba58115ab5cd503a5df7fab23169ebbfc150ab1ff7590303dd07f464c7f84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:07:44.197729Z","signature_b64":"HC3XLVjd544ml5SWGVbdsnK01wrjDM2Bvh5tzIcyMe2LIL7R1J4x0292lPsAKQS2l2DToKxjNPUjqU/A2WB8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0fba58115ab5cd503a5df7fab23169ebbfc150ab1ff7590303dd07f464c7f84","last_reissued_at":"2026-07-04T15:07:44.197362Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:07:44.197362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"dg-ga/9701011","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":"2026-07-04T15:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okoel0FY4/OAa7Ni+6EplQe+YdKfksHDZTZ89eZrAGH6kFq5yH8S4M5nronquaJuFt8R/LgTTA03XY6QLqKUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T22:39:57.265746Z"},"content_sha256":"f5b0b170dfb436c5140997b6f2c4ab59ff144b099bf481fadb534e88406c4017","schema_version":"1.0","event_id":"sha256:f5b0b170dfb436c5140997b6f2c4ab59ff144b099bf481fadb534e88406c4017"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:YD52LAIVVNONKA5F3572WIYWT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moduli Spaces of Stable Polygons and Symplectic Structures on $\\bar{M}_{0,n}$","license":"","headline":"","cross_cats":["alg-geom","math.AG","math.DG"],"primary_cat":"dg-ga","authors_text":"Yi Hu","submitted_at":"1997-01-27T22:46:22Z","abstract_excerpt":"In this paper, certain natural and elementary polygonal objects in Euclidean space, {\\it the stable polygons}, are introduced, and the novel moduli spaces ${\\bfmit M}_{{\\bf r}, \\epsilon}$ of stable polygons are constructed as complex analytic spaces. Quite unexpectedly, these new moduli spaces are shown to be projective and isomorphic to the moduli space $\\bar{\\cM}_{0,n}$ of the Deligne-Mumford stable curves of genus 0. Further, built into the structures of stable polygons are some natural data leading toward to a family of (classes of) symplectic (K\\\"ahler) forms. To some degree, ${\\bfmit M}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9701011","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/dg-ga/9701011/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":"2026-07-04T15:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBIw/Ef80qStG2B2lg8M+9v9v8pZJbSnoiHtPFQoPCoTJhj9w0L9eaGqrfBzGr6tuVECdumjEg+Baak/Tfo6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T22:39:57.266295Z"},"content_sha256":"36004c3914bc22ff64f3037b2d175e949044d7e54ae5b3d67af296ecf106109e","schema_version":"1.0","event_id":"sha256:36004c3914bc22ff64f3037b2d175e949044d7e54ae5b3d67af296ecf106109e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YD52LAIVVNONKA5F3572WIYWT2/bundle.json","state_url":"https://pith.science/pith/YD52LAIVVNONKA5F3572WIYWT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YD52LAIVVNONKA5F3572WIYWT2/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":"2026-08-06T22:39:57Z","links":{"resolver":"https://pith.science/pith/YD52LAIVVNONKA5F3572WIYWT2","bundle":"https://pith.science/pith/YD52LAIVVNONKA5F3572WIYWT2/bundle.json","state":"https://pith.science/pith/YD52LAIVVNONKA5F3572WIYWT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YD52LAIVVNONKA5F3572WIYWT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:YD52LAIVVNONKA5F3572WIYWT2","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":"60176392e2dc92a2038de91195d5415a20512b54dd3f3eb0cea3a7349ae2dacb","cross_cats_sorted":["alg-geom","math.AG","math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-01-27T22:46:22Z","title_canon_sha256":"84d5a0c27075cada7a66e39070b6b7dd326fcafd58be77bb4793f05b98bcb3df"},"schema_version":"1.0","source":{"id":"dg-ga/9701011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9701011","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9701011v2","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9701011","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"YD52LAIVVNON","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"pith_short_16","alias_value":"YD52LAIVVNONKA5F","created_at":"2026-07-04T15:07:44Z"},{"alias_kind":"pith_short_8","alias_value":"YD52LAIV","created_at":"2026-07-04T15:07:44Z"}],"graph_snapshots":[{"event_id":"sha256:36004c3914bc22ff64f3037b2d175e949044d7e54ae5b3d67af296ecf106109e","target":"graph","created_at":"2026-07-04T15:07:44Z","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/dg-ga/9701011/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, certain natural and elementary polygonal objects in Euclidean space, {\\it the stable polygons}, are introduced, and the novel moduli spaces ${\\bfmit M}_{{\\bf r}, \\epsilon}$ of stable polygons are constructed as complex analytic spaces. Quite unexpectedly, these new moduli spaces are shown to be projective and isomorphic to the moduli space $\\bar{\\cM}_{0,n}$ of the Deligne-Mumford stable curves of genus 0. Further, built into the structures of stable polygons are some natural data leading toward to a family of (classes of) symplectic (K\\\"ahler) forms. To some degree, ${\\bfmit M}_","authors_text":"Yi Hu","cross_cats":["alg-geom","math.AG","math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1997-01-27T22:46:22Z","title":"Moduli Spaces of Stable Polygons and Symplectic Structures on $\\bar{M}_{0,n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9701011","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:f5b0b170dfb436c5140997b6f2c4ab59ff144b099bf481fadb534e88406c4017","target":"record","created_at":"2026-07-04T15:07:44Z","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":"60176392e2dc92a2038de91195d5415a20512b54dd3f3eb0cea3a7349ae2dacb","cross_cats_sorted":["alg-geom","math.AG","math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-01-27T22:46:22Z","title_canon_sha256":"84d5a0c27075cada7a66e39070b6b7dd326fcafd58be77bb4793f05b98bcb3df"},"schema_version":"1.0","source":{"id":"dg-ga/9701011","kind":"arxiv","version":2}},"canonical_sha256":"c0fba58115ab5cd503a5df7fab23169ebbfc150ab1ff7590303dd07f464c7f84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0fba58115ab5cd503a5df7fab23169ebbfc150ab1ff7590303dd07f464c7f84","first_computed_at":"2026-07-04T15:07:44.197362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:07:44.197362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HC3XLVjd544ml5SWGVbdsnK01wrjDM2Bvh5tzIcyMe2LIL7R1J4x0292lPsAKQS2l2DToKxjNPUjqU/A2WB8Aw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:07:44.197729Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9701011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5b0b170dfb436c5140997b6f2c4ab59ff144b099bf481fadb534e88406c4017","sha256:36004c3914bc22ff64f3037b2d175e949044d7e54ae5b3d67af296ecf106109e"],"state_sha256":"a98b9f61fbc14dcf3738f950a1107bbf5327f0ff5494c273642fa0e8ec68f613"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65xcIN4D04wlU/2IQ8et7k9myrGKKLCaKBdgRfjhXKZTyg/OlzrjF1uHJJzVO2aJK8pV7JWfMRwBOhCqgvCQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T22:39:57.271731Z","bundle_sha256":"a28b325ca04780717df6d3779226c65e2fae9a1a979d5e82210259b9041faf3b"}}