{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EHOJ7VHCDRA6SMN5HFCGCZ7ZDD","short_pith_number":"pith:EHOJ7VHC","canonical_record":{"source":{"id":"1509.06406","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-21T21:27:14Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"0b63eed89be4bd1499a257cf8bdbc71328ad637e9dee73dcd5903eeabc7fed34","abstract_canon_sha256":"51563b12c71cd72dda486fa17eb26bd5ba08184af96985a7e3eab98e0a79cb7c"},"schema_version":"1.0"},"canonical_sha256":"21dc9fd4e21c41e931bd39446167f918cd2ca421ecb53873bd696bb4c3a7e39e","source":{"kind":"arxiv","id":"1509.06406","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06406","created_at":"2026-05-18T00:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06406v3","created_at":"2026-05-18T00:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06406","created_at":"2026-05-18T00:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"EHOJ7VHCDRA6","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EHOJ7VHCDRA6SMN5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EHOJ7VHC","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EHOJ7VHCDRA6SMN5HFCGCZ7ZDD","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06406","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-21T21:27:14Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"0b63eed89be4bd1499a257cf8bdbc71328ad637e9dee73dcd5903eeabc7fed34","abstract_canon_sha256":"51563b12c71cd72dda486fa17eb26bd5ba08184af96985a7e3eab98e0a79cb7c"},"schema_version":"1.0"},"canonical_sha256":"21dc9fd4e21c41e931bd39446167f918cd2ca421ecb53873bd696bb4c3a7e39e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:44.841737Z","signature_b64":"ETyxjVnk+1+Yvh3BzryVymQW5egYpkAHf69fMx2XO9hKnYTa+fKOd0gnXwpbaGXXH8S104rtQiSaahfvU7yYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21dc9fd4e21c41e931bd39446167f918cd2ca421ecb53873bd696bb4c3a7e39e","last_reissued_at":"2026-05-18T00:32:44.840969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:44.840969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06406","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sU0YYQ5m4Z1Maky/Q1w2JhaZP6XDiRr+A7Z90fZTKxVgoLh0sDhs/hwLVrEJk8fddC/3TGi5PzzQzqLc0RbSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:51:24.316741Z"},"content_sha256":"6ad509a4fd3f35ec006e8d27938cccadd76d11d214e7521a0d14f431289123e2","schema_version":"1.0","event_id":"sha256:6ad509a4fd3f35ec006e8d27938cccadd76d11d214e7521a0d14f431289123e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EHOJ7VHCDRA6SMN5HFCGCZ7ZDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contraction of Hamiltonian $K$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.SG","authors_text":"Christopher Manon, Joachim Hilgert, Johan Martens","submitted_at":"2015-09-21T21:27:14Z","abstract_excerpt":"In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We formulate an intrinsic symplectic contraction of a Hamiltonian space, which is a surjective, continuous map onto a new Hamiltonian space that is a symplectomorphism on an explicitly defined dense open subspace. This map is given by a precise formula, using techniques from the theory of symplectic reduction and symplectic implosion. We then show, using the Vinberg mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06406","kind":"arxiv","version":3},"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":"2026-05-18T00:32:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pxWYiZAsuDquidyP7JFdCNawXzINnrMww6dmrT80L6inIu/Ba5uL7PjBjI545vIb45pwAgmIgBDa9vfCUptSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:51:24.317394Z"},"content_sha256":"3f73c25e77d579163348034cdc161fccca39b67fda87e7b73811e91af442438b","schema_version":"1.0","event_id":"sha256:3f73c25e77d579163348034cdc161fccca39b67fda87e7b73811e91af442438b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD/bundle.json","state_url":"https://pith.science/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD/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":"2026-05-27T06:51:24Z","links":{"resolver":"https://pith.science/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD","bundle":"https://pith.science/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD/bundle.json","state":"https://pith.science/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHOJ7VHCDRA6SMN5HFCGCZ7ZDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EHOJ7VHCDRA6SMN5HFCGCZ7ZDD","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":"51563b12c71cd72dda486fa17eb26bd5ba08184af96985a7e3eab98e0a79cb7c","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-21T21:27:14Z","title_canon_sha256":"0b63eed89be4bd1499a257cf8bdbc71328ad637e9dee73dcd5903eeabc7fed34"},"schema_version":"1.0","source":{"id":"1509.06406","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06406","created_at":"2026-05-18T00:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06406v3","created_at":"2026-05-18T00:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06406","created_at":"2026-05-18T00:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"EHOJ7VHCDRA6","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EHOJ7VHCDRA6SMN5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EHOJ7VHC","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:3f73c25e77d579163348034cdc161fccca39b67fda87e7b73811e91af442438b","target":"graph","created_at":"2026-05-18T00:32:44Z","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"},"paper":{"abstract_excerpt":"In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We formulate an intrinsic symplectic contraction of a Hamiltonian space, which is a surjective, continuous map onto a new Hamiltonian space that is a symplectomorphism on an explicitly defined dense open subspace. This map is given by a precise formula, using techniques from the theory of symplectic reduction and symplectic implosion. We then show, using the Vinberg mo","authors_text":"Christopher Manon, Joachim Hilgert, Johan Martens","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-21T21:27:14Z","title":"Contraction of Hamiltonian $K$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06406","kind":"arxiv","version":3},"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":"sha256:6ad509a4fd3f35ec006e8d27938cccadd76d11d214e7521a0d14f431289123e2","target":"record","created_at":"2026-05-18T00:32:44Z","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":"51563b12c71cd72dda486fa17eb26bd5ba08184af96985a7e3eab98e0a79cb7c","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-21T21:27:14Z","title_canon_sha256":"0b63eed89be4bd1499a257cf8bdbc71328ad637e9dee73dcd5903eeabc7fed34"},"schema_version":"1.0","source":{"id":"1509.06406","kind":"arxiv","version":3}},"canonical_sha256":"21dc9fd4e21c41e931bd39446167f918cd2ca421ecb53873bd696bb4c3a7e39e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21dc9fd4e21c41e931bd39446167f918cd2ca421ecb53873bd696bb4c3a7e39e","first_computed_at":"2026-05-18T00:32:44.840969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:44.840969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ETyxjVnk+1+Yvh3BzryVymQW5egYpkAHf69fMx2XO9hKnYTa+fKOd0gnXwpbaGXXH8S104rtQiSaahfvU7yYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:44.841737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06406","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ad509a4fd3f35ec006e8d27938cccadd76d11d214e7521a0d14f431289123e2","sha256:3f73c25e77d579163348034cdc161fccca39b67fda87e7b73811e91af442438b"],"state_sha256":"adf78cf1f59444d959e3e67c18ac5fa56ef477f6ae433fe37dd56895eb74f048"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+IQLvnbVumR64tnqq+Wcizd06Sx2ykR+fb7UeDoZl40qtktnThhPzh1IrlGiBf+hpNK4LewFfTIx/ggvHJwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:51:24.321588Z","bundle_sha256":"f9ed6a3650d045726755d4306aaca4b979cbfc444f0becc76715895469ddfdd6"}}