{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:4HC365KZ7OVMV7PA7N47HIW4XY","short_pith_number":"pith:4HC365KZ","canonical_record":{"source":{"id":"math/0303122","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-03-11T04:01:54Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"cedfcfdc14e777aa4385ed7184bbee12776094f41ac04fa922b80c7abacd1628","abstract_canon_sha256":"4edbaaf23dbcbd01a725de18af66907586f8384207ab9ed91194cd3d90237c38"},"schema_version":"1.0"},"canonical_sha256":"e1c5bf7559fbaacafde0fb79f3a2dcbe205dbefdfb8b57e67d9b6c6fc4234621","source":{"kind":"arxiv","id":"math/0303122","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303122","created_at":"2026-05-18T01:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303122v2","created_at":"2026-05-18T01:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303122","created_at":"2026-05-18T01:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"4HC365KZ7OVM","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"4HC365KZ7OVMV7PA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"4HC365KZ","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:4HC365KZ7OVMV7PA7N47HIW4XY","target":"record","payload":{"canonical_record":{"source":{"id":"math/0303122","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-03-11T04:01:54Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"cedfcfdc14e777aa4385ed7184bbee12776094f41ac04fa922b80c7abacd1628","abstract_canon_sha256":"4edbaaf23dbcbd01a725de18af66907586f8384207ab9ed91194cd3d90237c38"},"schema_version":"1.0"},"canonical_sha256":"e1c5bf7559fbaacafde0fb79f3a2dcbe205dbefdfb8b57e67d9b6c6fc4234621","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:37.082778Z","signature_b64":"ZZCF9kBhuZ6RaRxZnOH7Dt37ASoRN8O3FqIgZEK847uRzb3YLHMCvCNwvF0lnH1YuUe0NMy413qTVKxT/O4QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1c5bf7559fbaacafde0fb79f3a2dcbe205dbefdfb8b57e67d9b6c6fc4234621","last_reissued_at":"2026-05-18T01:29:37.082136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:37.082136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0303122","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":"2026-05-18T01:29:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r9DYngyHSIVurvn3oHwxkujTMzhuJmsrfTKeAwckC6iYGb6BWaNf9fiRZLne8PnnnBCjZ0rXWp5e3iffDk5dAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:42.734407Z"},"content_sha256":"de4d532a9792c24a8bf7d664e9a6bef63af2b19236a7f69d2dfff7f1c0dbdd7e","schema_version":"1.0","event_id":"sha256:de4d532a9792c24a8bf7d664e9a6bef63af2b19236a7f69d2dfff7f1c0dbdd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:4HC365KZ7OVMV7PA7N47HIW4XY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metric transformations under collapsing of Riemannian manifolds","license":"","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Bennett Chow, David Glickenstein, Peng Lu","submitted_at":"2003-03-11T04:01:54Z","abstract_excerpt":"Let (M,g) be a Riemannian manifold with an isometric action of the Lie group G. Let g_G be a left invariant metric on G. Consider the diagonal G action on the product $M \\times G$ with the metric g+g_G. In this paper we calculate the formula for the metric h on the quotient space $(M \\times G) / G$; the map from g to h is the metric transformation. In particular when g is the hyperbolic metric on H^2 and G=S^1, the transformed metric h is Hamilton's cigar soliton metric studied in the Ricci flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303122","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":""},"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":"2026-05-18T01:29:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qz5Xs0n/ZH1MDG2Le6fElCqW0P8dxWrHNtdACPIDNcjav2OwwwWjptzPKUfxTxe4UioxrKfIg7eoRyc7GUgfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:42.735023Z"},"content_sha256":"539417baaa5709c349cfe6ef7f0a24a7a4758f4ebcce9ee9a135ebf453bd7eed","schema_version":"1.0","event_id":"sha256:539417baaa5709c349cfe6ef7f0a24a7a4758f4ebcce9ee9a135ebf453bd7eed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HC365KZ7OVMV7PA7N47HIW4XY/bundle.json","state_url":"https://pith.science/pith/4HC365KZ7OVMV7PA7N47HIW4XY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HC365KZ7OVMV7PA7N47HIW4XY/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":"2026-05-27T14:16:42Z","links":{"resolver":"https://pith.science/pith/4HC365KZ7OVMV7PA7N47HIW4XY","bundle":"https://pith.science/pith/4HC365KZ7OVMV7PA7N47HIW4XY/bundle.json","state":"https://pith.science/pith/4HC365KZ7OVMV7PA7N47HIW4XY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HC365KZ7OVMV7PA7N47HIW4XY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:4HC365KZ7OVMV7PA7N47HIW4XY","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":"4edbaaf23dbcbd01a725de18af66907586f8384207ab9ed91194cd3d90237c38","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2003-03-11T04:01:54Z","title_canon_sha256":"cedfcfdc14e777aa4385ed7184bbee12776094f41ac04fa922b80c7abacd1628"},"schema_version":"1.0","source":{"id":"math/0303122","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303122","created_at":"2026-05-18T01:29:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303122v2","created_at":"2026-05-18T01:29:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303122","created_at":"2026-05-18T01:29:37Z"},{"alias_kind":"pith_short_12","alias_value":"4HC365KZ7OVM","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"4HC365KZ7OVMV7PA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"4HC365KZ","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:539417baaa5709c349cfe6ef7f0a24a7a4758f4ebcce9ee9a135ebf453bd7eed","target":"graph","created_at":"2026-05-18T01:29:37Z","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 (M,g) be a Riemannian manifold with an isometric action of the Lie group G. Let g_G be a left invariant metric on G. Consider the diagonal G action on the product $M \\times G$ with the metric g+g_G. In this paper we calculate the formula for the metric h on the quotient space $(M \\times G) / G$; the map from g to h is the metric transformation. In particular when g is the hyperbolic metric on H^2 and G=S^1, the transformed metric h is Hamilton's cigar soliton metric studied in the Ricci flow.","authors_text":"Bennett Chow, David Glickenstein, Peng Lu","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2003-03-11T04:01:54Z","title":"Metric transformations under collapsing of Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303122","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:de4d532a9792c24a8bf7d664e9a6bef63af2b19236a7f69d2dfff7f1c0dbdd7e","target":"record","created_at":"2026-05-18T01:29:37Z","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":"4edbaaf23dbcbd01a725de18af66907586f8384207ab9ed91194cd3d90237c38","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2003-03-11T04:01:54Z","title_canon_sha256":"cedfcfdc14e777aa4385ed7184bbee12776094f41ac04fa922b80c7abacd1628"},"schema_version":"1.0","source":{"id":"math/0303122","kind":"arxiv","version":2}},"canonical_sha256":"e1c5bf7559fbaacafde0fb79f3a2dcbe205dbefdfb8b57e67d9b6c6fc4234621","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1c5bf7559fbaacafde0fb79f3a2dcbe205dbefdfb8b57e67d9b6c6fc4234621","first_computed_at":"2026-05-18T01:29:37.082136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:37.082136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZCF9kBhuZ6RaRxZnOH7Dt37ASoRN8O3FqIgZEK847uRzb3YLHMCvCNwvF0lnH1YuUe0NMy413qTVKxT/O4QDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:37.082778Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0303122","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de4d532a9792c24a8bf7d664e9a6bef63af2b19236a7f69d2dfff7f1c0dbdd7e","sha256:539417baaa5709c349cfe6ef7f0a24a7a4758f4ebcce9ee9a135ebf453bd7eed"],"state_sha256":"1ad9f168b597870930d639135d34156880e29c797bafa1738d7a3b58bfcd5acd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v3t/ErblqDuZ6jax+4gMOAce92B/TOaoAdf8tW6PEnuTjZAnBIMcYQQwf9bqHmqLbalc4zq59gMHJFx7zXKOCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:16:42.737600Z","bundle_sha256":"231147f9cbf2392631c3d343b611161f096163def0ecc561d2909042846510e3"}}