{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M73EBFHHNHBMXGBAVBHUF53ABV","short_pith_number":"pith:M73EBFHH","canonical_record":{"source":{"id":"1407.2665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-10T01:23:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"88dfa1ecad34c21514a7f43d1ff98c9781f35c33ee3d36382d841a21c99e21d9","abstract_canon_sha256":"7a4f617453ddacaba3c18ab126966b700aab279273df71d5cd8956268a19a04b"},"schema_version":"1.0"},"canonical_sha256":"67f64094e769c2cb9820a84f42f7600d58d77a3b98855b0e37dfba6f5677a736","source":{"kind":"arxiv","id":"1407.2665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2665","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2665v1","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2665","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"M73EBFHHNHBM","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M73EBFHHNHBMXGBA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M73EBFHH","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M73EBFHHNHBMXGBAVBHUF53ABV","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-10T01:23:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"88dfa1ecad34c21514a7f43d1ff98c9781f35c33ee3d36382d841a21c99e21d9","abstract_canon_sha256":"7a4f617453ddacaba3c18ab126966b700aab279273df71d5cd8956268a19a04b"},"schema_version":"1.0"},"canonical_sha256":"67f64094e769c2cb9820a84f42f7600d58d77a3b98855b0e37dfba6f5677a736","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.986283Z","signature_b64":"c9Z2WnVUqM2MtF1LgSCFAEyUm7OaHgcIrRfepHZNrq+pCqEMKf+aBFJU2BX6YE9Y5mR5i2ZW9/eK14pRwkhMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67f64094e769c2cb9820a84f42f7600d58d77a3b98855b0e37dfba6f5677a736","last_reissued_at":"2026-05-18T02:47:53.985715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.985715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2665","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":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R4xFnY0P4tkzfU1qblvBJgJDZF38r1T/AlmXxpxrysrJvMsmL9/p0qvQGy4+r0jv8p56BBw694jM0xpASLhyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:51:48.495410Z"},"content_sha256":"ad45fd04d8617ce8400ecece47d52c86c83bbbfacbb64db3138eee3692a91028","schema_version":"1.0","event_id":"sha256:ad45fd04d8617ce8400ecece47d52c86c83bbbfacbb64db3138eee3692a91028"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M73EBFHHNHBMXGBAVBHUF53ABV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Top-stable degenerations of finite dimensional representations I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Birge Huisgen-Zimmermann","submitted_at":"2014-07-10T01:23:17Z","abstract_excerpt":"Given a finite dimensional representation $M$ of a finite dimensional algebra, two hierarchies of degenerations of $M$ are analyzed in the context of their natural orders: the poset of those degenerations of $M$ which share the top $M/JM$ with $M$ - here $J$ denotes the radical of the algebra - and the sub-poset of those which share the full radical layering $\\bigl(J^lM/J^{l+1}M\\bigr)_{l \\ge 0}$ with $M$. In particular, the article addresses existence of proper top-stable or layer-stable degenerations - more generally, it addresses the sizes of the corresponding posets including bounds on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2665","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":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oTasM3qdXCMmaBArOHZKCt6D36Nya6Py/5zMz7Q/iWh4bnwKq8wfP8ItrCKy4euAAP8nn1XVxwfdCU8Ps+srDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:51:48.495820Z"},"content_sha256":"072d8eae69fd7dff0e79324512e2ef213ae4558ba0d2eb32f398348f27e3f803","schema_version":"1.0","event_id":"sha256:072d8eae69fd7dff0e79324512e2ef213ae4558ba0d2eb32f398348f27e3f803"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M73EBFHHNHBMXGBAVBHUF53ABV/bundle.json","state_url":"https://pith.science/pith/M73EBFHHNHBMXGBAVBHUF53ABV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M73EBFHHNHBMXGBAVBHUF53ABV/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":"2026-05-31T20:51:48Z","links":{"resolver":"https://pith.science/pith/M73EBFHHNHBMXGBAVBHUF53ABV","bundle":"https://pith.science/pith/M73EBFHHNHBMXGBAVBHUF53ABV/bundle.json","state":"https://pith.science/pith/M73EBFHHNHBMXGBAVBHUF53ABV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M73EBFHHNHBMXGBAVBHUF53ABV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M73EBFHHNHBMXGBAVBHUF53ABV","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":"7a4f617453ddacaba3c18ab126966b700aab279273df71d5cd8956268a19a04b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-10T01:23:17Z","title_canon_sha256":"88dfa1ecad34c21514a7f43d1ff98c9781f35c33ee3d36382d841a21c99e21d9"},"schema_version":"1.0","source":{"id":"1407.2665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2665","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2665v1","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2665","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"M73EBFHHNHBM","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M73EBFHHNHBMXGBA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M73EBFHH","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:072d8eae69fd7dff0e79324512e2ef213ae4558ba0d2eb32f398348f27e3f803","target":"graph","created_at":"2026-05-18T02:47:53Z","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":"Given a finite dimensional representation $M$ of a finite dimensional algebra, two hierarchies of degenerations of $M$ are analyzed in the context of their natural orders: the poset of those degenerations of $M$ which share the top $M/JM$ with $M$ - here $J$ denotes the radical of the algebra - and the sub-poset of those which share the full radical layering $\\bigl(J^lM/J^{l+1}M\\bigr)_{l \\ge 0}$ with $M$. In particular, the article addresses existence of proper top-stable or layer-stable degenerations - more generally, it addresses the sizes of the corresponding posets including bounds on the ","authors_text":"Birge Huisgen-Zimmermann","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-10T01:23:17Z","title":"Top-stable degenerations of finite dimensional representations I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2665","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:ad45fd04d8617ce8400ecece47d52c86c83bbbfacbb64db3138eee3692a91028","target":"record","created_at":"2026-05-18T02:47:53Z","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":"7a4f617453ddacaba3c18ab126966b700aab279273df71d5cd8956268a19a04b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-10T01:23:17Z","title_canon_sha256":"88dfa1ecad34c21514a7f43d1ff98c9781f35c33ee3d36382d841a21c99e21d9"},"schema_version":"1.0","source":{"id":"1407.2665","kind":"arxiv","version":1}},"canonical_sha256":"67f64094e769c2cb9820a84f42f7600d58d77a3b98855b0e37dfba6f5677a736","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67f64094e769c2cb9820a84f42f7600d58d77a3b98855b0e37dfba6f5677a736","first_computed_at":"2026-05-18T02:47:53.985715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:53.985715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c9Z2WnVUqM2MtF1LgSCFAEyUm7OaHgcIrRfepHZNrq+pCqEMKf+aBFJU2BX6YE9Y5mR5i2ZW9/eK14pRwkhMAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:53.986283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad45fd04d8617ce8400ecece47d52c86c83bbbfacbb64db3138eee3692a91028","sha256:072d8eae69fd7dff0e79324512e2ef213ae4558ba0d2eb32f398348f27e3f803"],"state_sha256":"9fc8cfa981e95d62279c97bd1e158b375348e7548894d66025ec09f468925fcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"36fN0sI5CyzWNvTC+2WQ14Vl6vxdAGmzE23TjRozQCdRBd4QLw41xJ5YS8FMfK2RECHEqUKkQysG/VUGZz6zCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:51:48.498351Z","bundle_sha256":"4fee1f19938c2b108e1203b121b30f819a2186be0d0cf46442e31c668fd6d4bf"}}