{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GNVO6CZUJFZPWZQZIRB4O6RBPG","short_pith_number":"pith:GNVO6CZU","canonical_record":{"source":{"id":"1204.3031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T15:50:49Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"cb59b358f702ad55562d714aa66b14294d8758d963ff519b4e7aa744ccfd1564","abstract_canon_sha256":"df67e727b958d143b1c83383d15ef00cf6b03b8143db6c714c61dfe6bc9e22ec"},"schema_version":"1.0"},"canonical_sha256":"336aef0b344972fb66194443c77a217983a8bd32bb2ef670ece4c458752fc195","source":{"kind":"arxiv","id":"1204.3031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3031","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3031v1","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3031","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"GNVO6CZUJFZP","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GNVO6CZUJFZPWZQZ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GNVO6CZU","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GNVO6CZUJFZPWZQZIRB4O6RBPG","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T15:50:49Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"cb59b358f702ad55562d714aa66b14294d8758d963ff519b4e7aa744ccfd1564","abstract_canon_sha256":"df67e727b958d143b1c83383d15ef00cf6b03b8143db6c714c61dfe6bc9e22ec"},"schema_version":"1.0"},"canonical_sha256":"336aef0b344972fb66194443c77a217983a8bd32bb2ef670ece4c458752fc195","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:54.103704Z","signature_b64":"72phdTF+zkfDftutqc3SuQd/wnXdXy5OgCc1IYeP8ZgfyJIqADXsyzwmzq46DE8/kgvLfV2ynMJkZdwvFzXDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"336aef0b344972fb66194443c77a217983a8bd32bb2ef670ece4c458752fc195","last_reissued_at":"2026-05-18T03:57:54.102910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:54.102910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3031","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":"2026-05-18T03:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7ppkGbffa1Rs7uKBBIXE6gww8oQU6lr/K7HHxdDAOBxw4Ih+EfdMnxeic4yJHIdl25bHvwoggUo+ae6wMSqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:51:31.358399Z"},"content_sha256":"eb13880d85b4599ee7cfa055f11effdf8e172ae9e3405d080fea883284b2a70c","schema_version":"1.0","event_id":"sha256:eb13880d85b4599ee7cfa055f11effdf8e172ae9e3405d080fea883284b2a70c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GNVO6CZUJFZPWZQZIRB4O6RBPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of nilsolitons on 2-step nilpotent Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"David Oscari","submitted_at":"2012-04-13T15:50:49Z","abstract_excerpt":"A 2-step nilpotent Lie algebra n is said to be of type (p,q)if dim(n)=p+q and dim([n,n])=p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there exist indecomposable, 2-step nilpotent Lie groups of type (p,q) which do not admit a nilsoliton metric for every pair (p,q) such that 20 < q and q-2 < p < 1/2q^2-5/2q+10. This improves a result due to Jablonski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3031","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":"2026-05-18T03:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbbzW73ls7zQrvdAzeezANH3RexxLHzS0Mk0i3bpMEr6ACWq53WyMfPORbTTFaDbDWIuxSrP4mTgKu+Q2gADAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:51:31.358778Z"},"content_sha256":"6689c1d90e8a4a9bcd76400eb87e9a04d2b709884b251d37610a7b0fe8a9e6c3","schema_version":"1.0","event_id":"sha256:6689c1d90e8a4a9bcd76400eb87e9a04d2b709884b251d37610a7b0fe8a9e6c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG/bundle.json","state_url":"https://pith.science/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG/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":"2026-06-23T07:51:31Z","links":{"resolver":"https://pith.science/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG","bundle":"https://pith.science/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG/bundle.json","state":"https://pith.science/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNVO6CZUJFZPWZQZIRB4O6RBPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GNVO6CZUJFZPWZQZIRB4O6RBPG","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":"df67e727b958d143b1c83383d15ef00cf6b03b8143db6c714c61dfe6bc9e22ec","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T15:50:49Z","title_canon_sha256":"cb59b358f702ad55562d714aa66b14294d8758d963ff519b4e7aa744ccfd1564"},"schema_version":"1.0","source":{"id":"1204.3031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3031","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3031v1","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3031","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"GNVO6CZUJFZP","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GNVO6CZUJFZPWZQZ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GNVO6CZU","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:6689c1d90e8a4a9bcd76400eb87e9a04d2b709884b251d37610a7b0fe8a9e6c3","target":"graph","created_at":"2026-05-18T03:57:54Z","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":"A 2-step nilpotent Lie algebra n is said to be of type (p,q)if dim(n)=p+q and dim([n,n])=p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there exist indecomposable, 2-step nilpotent Lie groups of type (p,q) which do not admit a nilsoliton metric for every pair (p,q) such that 20 < q and q-2 < p < 1/2q^2-5/2q+10. This improves a result due to Jablonski.","authors_text":"David Oscari","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T15:50:49Z","title":"On the existence of nilsolitons on 2-step nilpotent Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3031","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:eb13880d85b4599ee7cfa055f11effdf8e172ae9e3405d080fea883284b2a70c","target":"record","created_at":"2026-05-18T03:57:54Z","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":"df67e727b958d143b1c83383d15ef00cf6b03b8143db6c714c61dfe6bc9e22ec","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-13T15:50:49Z","title_canon_sha256":"cb59b358f702ad55562d714aa66b14294d8758d963ff519b4e7aa744ccfd1564"},"schema_version":"1.0","source":{"id":"1204.3031","kind":"arxiv","version":1}},"canonical_sha256":"336aef0b344972fb66194443c77a217983a8bd32bb2ef670ece4c458752fc195","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"336aef0b344972fb66194443c77a217983a8bd32bb2ef670ece4c458752fc195","first_computed_at":"2026-05-18T03:57:54.102910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:54.102910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"72phdTF+zkfDftutqc3SuQd/wnXdXy5OgCc1IYeP8ZgfyJIqADXsyzwmzq46DE8/kgvLfV2ynMJkZdwvFzXDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:54.103704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb13880d85b4599ee7cfa055f11effdf8e172ae9e3405d080fea883284b2a70c","sha256:6689c1d90e8a4a9bcd76400eb87e9a04d2b709884b251d37610a7b0fe8a9e6c3"],"state_sha256":"4ab2da5992f062d57d54f057a352f447b424746711e04ea6e3210eb1015a91a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ua18eHTdVj0lD7akkid5jexKALKpQ7tbP2yRCZmWINYNW/4CtthbtDky/NnN4tNt4bshptzD4dhoOHKwILObBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:51:31.360749Z","bundle_sha256":"2dcedc87fa2b6b640cdfd10998f0f54539138108f14811f3bb2289b1c89fdc53"}}