{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:BM76U3XAOZ2RF4G2NEJGFYYAMM","short_pith_number":"pith:BM76U3XA","canonical_record":{"source":{"id":"math/0611075","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-11-03T13:32:00Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bcfb2946efc4ee133bba3810b0fb46fea19f412bc0775a070a6b26c6f617bfdd","abstract_canon_sha256":"f1f957d6ec6561da5797136f20b9f6edc6531f3d267f49ae346d22c4912350bf"},"schema_version":"1.0"},"canonical_sha256":"0b3fea6ee0767512f0da691262e300633e7cce17c6bb696bbc41e6647deba036","source":{"kind":"arxiv","id":"math/0611075","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611075","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611075v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611075","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"BM76U3XAOZ2R","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"BM76U3XAOZ2RF4G2","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"BM76U3XA","created_at":"2026-06-03T22:06:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:BM76U3XAOZ2RF4G2NEJGFYYAMM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611075","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-11-03T13:32:00Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bcfb2946efc4ee133bba3810b0fb46fea19f412bc0775a070a6b26c6f617bfdd","abstract_canon_sha256":"f1f957d6ec6561da5797136f20b9f6edc6531f3d267f49ae346d22c4912350bf"},"schema_version":"1.0"},"canonical_sha256":"0b3fea6ee0767512f0da691262e300633e7cce17c6bb696bbc41e6647deba036","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:21.043490Z","signature_b64":"h/y6Bxo7XjkfF2BZq63WQ6a3P01fa1Lfjof9JbShqa08OyTzKkiPYnBXyFdcxuCuVubOn4OZn8gsbU99P62WAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b3fea6ee0767512f0da691262e300633e7cce17c6bb696bbc41e6647deba036","last_reissued_at":"2026-06-03T22:06:21.043073Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:21.043073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611075","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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9s1KjZUpPm6o1mj9Hc9kVKXbIm5sCKJhstWZb1VQtIaD/RD9TZJeQ7LzW5S/GDXAlj/WWsWfMJi3NEiT8GkfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:15:41.403049Z"},"content_sha256":"a9058e521dda1ac376651ccef0d12770e623ff34f076789f3c5da4120eacb6e9","schema_version":"1.0","event_id":"sha256:a9058e521dda1ac376651ccef0d12770e623ff34f076789f3c5da4120eacb6e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:BM76U3XAOZ2RF4G2NEJGFYYAMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysing singularities of a benchmark problem","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jukka Tuomela, Samuli Piipponen, Teijo Arponen","submitted_at":"2006-11-03T13:32:00Z","abstract_excerpt":"The purpose of this paper is to analyze the singularities of a well known benchmark problem ``Andrews' squeezing mechanism''. We show that for physically relevant parameter values this system admits singularities. The method is based on Gr\\\"obner bases computations and ideal decomposition. It is algorithmic and can thus be applied to study constraint singularities which arise in more general situations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611075","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0611075/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ny37Y55AlO+LodiBkFh6ZeznnuHic76Jkki9ioKDph1231hx2y0BZOOPl0srKt2IyFMrad2+oaSKGQDAGbqbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:15:41.403439Z"},"content_sha256":"6bfc8f9f905d687ce51b3c493558bf0f27d223fe623bdf1ba62c8f304e325e1c","schema_version":"1.0","event_id":"sha256:6bfc8f9f905d687ce51b3c493558bf0f27d223fe623bdf1ba62c8f304e325e1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM/bundle.json","state_url":"https://pith.science/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM/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":"2026-06-28T12:15:41Z","links":{"resolver":"https://pith.science/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM","bundle":"https://pith.science/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM/bundle.json","state":"https://pith.science/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BM76U3XAOZ2RF4G2NEJGFYYAMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:BM76U3XAOZ2RF4G2NEJGFYYAMM","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":"f1f957d6ec6561da5797136f20b9f6edc6531f3d267f49ae346d22c4912350bf","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2006-11-03T13:32:00Z","title_canon_sha256":"bcfb2946efc4ee133bba3810b0fb46fea19f412bc0775a070a6b26c6f617bfdd"},"schema_version":"1.0","source":{"id":"math/0611075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611075","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611075v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611075","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"BM76U3XAOZ2R","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"BM76U3XAOZ2RF4G2","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"BM76U3XA","created_at":"2026-06-03T22:06:21Z"}],"graph_snapshots":[{"event_id":"sha256:6bfc8f9f905d687ce51b3c493558bf0f27d223fe623bdf1ba62c8f304e325e1c","target":"graph","created_at":"2026-06-03T22:06:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0611075/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is to analyze the singularities of a well known benchmark problem ``Andrews' squeezing mechanism''. We show that for physically relevant parameter values this system admits singularities. The method is based on Gr\\\"obner bases computations and ideal decomposition. It is algorithmic and can thus be applied to study constraint singularities which arise in more general situations.","authors_text":"Jukka Tuomela, Samuli Piipponen, Teijo Arponen","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2006-11-03T13:32:00Z","title":"Analysing singularities of a benchmark problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611075","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:a9058e521dda1ac376651ccef0d12770e623ff34f076789f3c5da4120eacb6e9","target":"record","created_at":"2026-06-03T22:06:21Z","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":"f1f957d6ec6561da5797136f20b9f6edc6531f3d267f49ae346d22c4912350bf","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2006-11-03T13:32:00Z","title_canon_sha256":"bcfb2946efc4ee133bba3810b0fb46fea19f412bc0775a070a6b26c6f617bfdd"},"schema_version":"1.0","source":{"id":"math/0611075","kind":"arxiv","version":1}},"canonical_sha256":"0b3fea6ee0767512f0da691262e300633e7cce17c6bb696bbc41e6647deba036","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b3fea6ee0767512f0da691262e300633e7cce17c6bb696bbc41e6647deba036","first_computed_at":"2026-06-03T22:06:21.043073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:21.043073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h/y6Bxo7XjkfF2BZq63WQ6a3P01fa1Lfjof9JbShqa08OyTzKkiPYnBXyFdcxuCuVubOn4OZn8gsbU99P62WAA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:21.043490Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9058e521dda1ac376651ccef0d12770e623ff34f076789f3c5da4120eacb6e9","sha256:6bfc8f9f905d687ce51b3c493558bf0f27d223fe623bdf1ba62c8f304e325e1c"],"state_sha256":"93df94e8686a6741f8bac40a6a59fd9724c0816a78455aeb5ca21ff875f78910"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9i8+jqxlg1+3LzEwXgZ7kkGDhViiH7dptgewrmoEpQuzecQjOyljWPgRt8JNTVPu4v91GAq63u+sXyjmNlhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:15:41.405355Z","bundle_sha256":"892590d17aadc1dc0e297ed1ebf12b18b6f029962c5ceb4c4498abf43a9cb057"}}