{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YCG6JCZ6ZJ7PG6MANC5HFTIBDU","short_pith_number":"pith:YCG6JCZ6","canonical_record":{"source":{"id":"1505.02939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-12T09:56:10Z","cross_cats_sorted":["math.CV","math.GT"],"title_canon_sha256":"4e7e9349770dab52de4fd08f30d1de45e5797ffc75809409beea1813e86c1664","abstract_canon_sha256":"d96e9a8efe9d1515ad1514e5ca9de5ba7d91c68886ece772dec8b3ba0061d763"},"schema_version":"1.0"},"canonical_sha256":"c08de48b3eca7ef3798068ba72cd011d3feafd19997554cbdda0a3d89ac0f109","source":{"kind":"arxiv","id":"1505.02939","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02939","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02939v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02939","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"YCG6JCZ6ZJ7P","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCG6JCZ6ZJ7PG6MA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCG6JCZ6","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YCG6JCZ6ZJ7PG6MANC5HFTIBDU","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-12T09:56:10Z","cross_cats_sorted":["math.CV","math.GT"],"title_canon_sha256":"4e7e9349770dab52de4fd08f30d1de45e5797ffc75809409beea1813e86c1664","abstract_canon_sha256":"d96e9a8efe9d1515ad1514e5ca9de5ba7d91c68886ece772dec8b3ba0061d763"},"schema_version":"1.0"},"canonical_sha256":"c08de48b3eca7ef3798068ba72cd011d3feafd19997554cbdda0a3d89ac0f109","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:15.573226Z","signature_b64":"4cTgn6UNe7C/+eE2Z6UvfmAwv4tTaFYwxzt0KaHD+Ckm2XpBSj5GXU+4JK/dTptwmTIh+ypIfcqpC/tNtCT4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c08de48b3eca7ef3798068ba72cd011d3feafd19997554cbdda0a3d89ac0f109","last_reissued_at":"2026-05-18T02:14:15.572433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:15.572433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02939","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":"2026-05-18T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FvIP+wm4LBqGKly/cG97+WoLxeWDY9imX7/oUrw/C4QDDUybDuEjmXp31mjcrVM2/JTpoTkVqFKZkukU7Ju8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:00:15.648274Z"},"content_sha256":"c241137fa8eec764ea7c7869847b3185a9b19891913ce765f3b79899c2213c0c","schema_version":"1.0","event_id":"sha256:c241137fa8eec764ea7c7869847b3185a9b19891913ce765f3b79899c2213c0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YCG6JCZ6ZJ7PG6MANC5HFTIBDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic differentials, half-plane structures, and harmonic maps to graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.DG","authors_text":"Michael Wolf, Subhojoy Gupta","submitted_at":"2015-05-12T09:56:10Z","abstract_excerpt":"Let $(\\Sigma,p)$ be a pointed Riemann surface of genus $g\\geq 1$. For any integer $k\\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph and an induced metric composed of $k$ Euclidean half-planes. The parameters form a finite-dimensional space $\\mathcal{L} \\cong \\mathbb{R}^{k} \\times S^1$ that describe a model singular-flat metric around the puncture with respect to a choice of coordinate chart. This generalizes an important theorem of Strebel, and associates, to each point in a decorated Te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02939","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":"2026-05-18T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9KS9CFOgQqpMMOXsIPk1pJiIIBNSHL3kFl4i5e260rpIdnT7vYlUs4wijV6INSdr0mbR3bX2JY7PUjwtgHGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:00:15.648654Z"},"content_sha256":"0331556bc053c279d18e4fc19c25b2a571eb24feb6d005b904030d1769da859f","schema_version":"1.0","event_id":"sha256:0331556bc053c279d18e4fc19c25b2a571eb24feb6d005b904030d1769da859f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU/bundle.json","state_url":"https://pith.science/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU/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":"2026-06-03T11:00:15Z","links":{"resolver":"https://pith.science/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU","bundle":"https://pith.science/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU/bundle.json","state":"https://pith.science/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCG6JCZ6ZJ7PG6MANC5HFTIBDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YCG6JCZ6ZJ7PG6MANC5HFTIBDU","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":"d96e9a8efe9d1515ad1514e5ca9de5ba7d91c68886ece772dec8b3ba0061d763","cross_cats_sorted":["math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-12T09:56:10Z","title_canon_sha256":"4e7e9349770dab52de4fd08f30d1de45e5797ffc75809409beea1813e86c1664"},"schema_version":"1.0","source":{"id":"1505.02939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02939","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02939v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02939","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"YCG6JCZ6ZJ7P","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YCG6JCZ6ZJ7PG6MA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YCG6JCZ6","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:0331556bc053c279d18e4fc19c25b2a571eb24feb6d005b904030d1769da859f","target":"graph","created_at":"2026-05-18T02:14:15Z","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 $(\\Sigma,p)$ be a pointed Riemann surface of genus $g\\geq 1$. For any integer $k\\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph and an induced metric composed of $k$ Euclidean half-planes. The parameters form a finite-dimensional space $\\mathcal{L} \\cong \\mathbb{R}^{k} \\times S^1$ that describe a model singular-flat metric around the puncture with respect to a choice of coordinate chart. This generalizes an important theorem of Strebel, and associates, to each point in a decorated Te","authors_text":"Michael Wolf, Subhojoy Gupta","cross_cats":["math.CV","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-12T09:56:10Z","title":"Quadratic differentials, half-plane structures, and harmonic maps to graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02939","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:c241137fa8eec764ea7c7869847b3185a9b19891913ce765f3b79899c2213c0c","target":"record","created_at":"2026-05-18T02:14:15Z","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":"d96e9a8efe9d1515ad1514e5ca9de5ba7d91c68886ece772dec8b3ba0061d763","cross_cats_sorted":["math.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-12T09:56:10Z","title_canon_sha256":"4e7e9349770dab52de4fd08f30d1de45e5797ffc75809409beea1813e86c1664"},"schema_version":"1.0","source":{"id":"1505.02939","kind":"arxiv","version":1}},"canonical_sha256":"c08de48b3eca7ef3798068ba72cd011d3feafd19997554cbdda0a3d89ac0f109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c08de48b3eca7ef3798068ba72cd011d3feafd19997554cbdda0a3d89ac0f109","first_computed_at":"2026-05-18T02:14:15.572433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:15.572433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4cTgn6UNe7C/+eE2Z6UvfmAwv4tTaFYwxzt0KaHD+Ckm2XpBSj5GXU+4JK/dTptwmTIh+ypIfcqpC/tNtCT4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:15.573226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c241137fa8eec764ea7c7869847b3185a9b19891913ce765f3b79899c2213c0c","sha256:0331556bc053c279d18e4fc19c25b2a571eb24feb6d005b904030d1769da859f"],"state_sha256":"a5dd423bcfcab31553276d202f4d5aaca97ee1db6b457ec9ec76caa3ee46dd48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"747p2nfRD1YmtieQaDgXJv56246aHz78sZuZR/x8VFN/wloF9T4UIDtuLWMX4ho40StqhcFwWbjgb8Zt172YDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:00:15.650626Z","bundle_sha256":"ac3fb718d5bd783939c094fcbaacb4667408307a9429d6fad87d693e3e7bf1f8"}}