{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7COSRYHMFNYUWVOZMB74NYOB3F","short_pith_number":"pith:7COSRYHM","canonical_record":{"source":{"id":"1010.5552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-27T02:17:49Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"cc394eb4c0805eece5bfa64fd72c94f6f85d8fb58efdabd99ccf862d451e3527","abstract_canon_sha256":"8dd5831ace7d998f9ef658932a818152284f6dfb8235d9d42ed8e5f86e31066c"},"schema_version":"1.0"},"canonical_sha256":"f89d28e0ec2b714b55d9607fc6e1c1d96f35733f9556c6d70647a09c2af3188f","source":{"kind":"arxiv","id":"1010.5552","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5552","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5552v2","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5552","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"7COSRYHMFNYU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7COSRYHMFNYUWVOZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7COSRYHM","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7COSRYHMFNYUWVOZMB74NYOB3F","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-27T02:17:49Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"cc394eb4c0805eece5bfa64fd72c94f6f85d8fb58efdabd99ccf862d451e3527","abstract_canon_sha256":"8dd5831ace7d998f9ef658932a818152284f6dfb8235d9d42ed8e5f86e31066c"},"schema_version":"1.0"},"canonical_sha256":"f89d28e0ec2b714b55d9607fc6e1c1d96f35733f9556c6d70647a09c2af3188f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:38.501308Z","signature_b64":"qPmeILeF+brQ2L4jytkBITKbT6YPd0xDIT9k4rtpzuXChJmRtoatX/d22fU9B97Laz6Yyf2sfTpKX7F3USHCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f89d28e0ec2b714b55d9607fc6e1c1d96f35733f9556c6d70647a09c2af3188f","last_reissued_at":"2026-05-18T02:23:38.500865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:38.500865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5552","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tg2jVdsSDwv1EWgJRhXfXzYp6rNUiV4WAzp35OvoYZ/pMl0jlY0feN6GDYYspo1QVNYvg7vz16TtLDFHjjN2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:21:27.762772Z"},"content_sha256":"87913e320575a222702abb3177bc1436ed0846be2084b5b2fee98e83e6073f4b","schema_version":"1.0","event_id":"sha256:87913e320575a222702abb3177bc1436ed0846be2084b5b2fee98e83e6073f4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7COSRYHMFNYUWVOZMB74NYOB3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Directed Graphs, Decompositions, and Spatial Linkages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Adnan Sljoka, Offer Shai, Walter Whiteley","submitted_at":"2010-10-27T02:17:49Z","abstract_excerpt":"The decomposition of a linkage into minimal components is a central tool of analysis and synthesis of linkages. In this paper we prove that every pinned d-isostatic (minimally rigid) graph (grounded linkage) has a unique decomposition into minimal strongly connected components (in the sense of directed graphs), or equivalently into minimal pinned isostatic graphs, which we call d-Assur graphs. We also study key properties of motions induced by removing an edge in a d-Assur graph - defining a stronger sub-class of strongly d-Assur graphs by the property that all inner vertices go into motion, f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5552","kind":"arxiv","version":2},"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":"2026-05-18T02:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+ObwIfQslCC5hionJOMBG8eBCiQL3r+NTBZExOzwyKoAX0LwaU34Il3FgaAJkA485ypLgbKyi+JTM1JM7s2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:21:27.763125Z"},"content_sha256":"b033622f71af068d78c609cf24ddbfc6b0c58928117876746cadd3094e2463a6","schema_version":"1.0","event_id":"sha256:b033622f71af068d78c609cf24ddbfc6b0c58928117876746cadd3094e2463a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7COSRYHMFNYUWVOZMB74NYOB3F/bundle.json","state_url":"https://pith.science/pith/7COSRYHMFNYUWVOZMB74NYOB3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7COSRYHMFNYUWVOZMB74NYOB3F/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":"2026-06-02T23:21:27Z","links":{"resolver":"https://pith.science/pith/7COSRYHMFNYUWVOZMB74NYOB3F","bundle":"https://pith.science/pith/7COSRYHMFNYUWVOZMB74NYOB3F/bundle.json","state":"https://pith.science/pith/7COSRYHMFNYUWVOZMB74NYOB3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7COSRYHMFNYUWVOZMB74NYOB3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7COSRYHMFNYUWVOZMB74NYOB3F","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":"8dd5831ace7d998f9ef658932a818152284f6dfb8235d9d42ed8e5f86e31066c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-27T02:17:49Z","title_canon_sha256":"cc394eb4c0805eece5bfa64fd72c94f6f85d8fb58efdabd99ccf862d451e3527"},"schema_version":"1.0","source":{"id":"1010.5552","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5552","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5552v2","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5552","created_at":"2026-05-18T02:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"7COSRYHMFNYU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7COSRYHMFNYUWVOZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7COSRYHM","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:b033622f71af068d78c609cf24ddbfc6b0c58928117876746cadd3094e2463a6","target":"graph","created_at":"2026-05-18T02:23:38Z","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":"The decomposition of a linkage into minimal components is a central tool of analysis and synthesis of linkages. In this paper we prove that every pinned d-isostatic (minimally rigid) graph (grounded linkage) has a unique decomposition into minimal strongly connected components (in the sense of directed graphs), or equivalently into minimal pinned isostatic graphs, which we call d-Assur graphs. We also study key properties of motions induced by removing an edge in a d-Assur graph - defining a stronger sub-class of strongly d-Assur graphs by the property that all inner vertices go into motion, f","authors_text":"Adnan Sljoka, Offer Shai, Walter Whiteley","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-27T02:17:49Z","title":"Directed Graphs, Decompositions, and Spatial Linkages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5552","kind":"arxiv","version":2},"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":"sha256:87913e320575a222702abb3177bc1436ed0846be2084b5b2fee98e83e6073f4b","target":"record","created_at":"2026-05-18T02:23:38Z","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":"8dd5831ace7d998f9ef658932a818152284f6dfb8235d9d42ed8e5f86e31066c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-27T02:17:49Z","title_canon_sha256":"cc394eb4c0805eece5bfa64fd72c94f6f85d8fb58efdabd99ccf862d451e3527"},"schema_version":"1.0","source":{"id":"1010.5552","kind":"arxiv","version":2}},"canonical_sha256":"f89d28e0ec2b714b55d9607fc6e1c1d96f35733f9556c6d70647a09c2af3188f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f89d28e0ec2b714b55d9607fc6e1c1d96f35733f9556c6d70647a09c2af3188f","first_computed_at":"2026-05-18T02:23:38.500865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:38.500865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPmeILeF+brQ2L4jytkBITKbT6YPd0xDIT9k4rtpzuXChJmRtoatX/d22fU9B97Laz6Yyf2sfTpKX7F3USHCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:38.501308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5552","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87913e320575a222702abb3177bc1436ed0846be2084b5b2fee98e83e6073f4b","sha256:b033622f71af068d78c609cf24ddbfc6b0c58928117876746cadd3094e2463a6"],"state_sha256":"676c2bd1316fd3aecd32c2d7ea454cf7fbf5e6013b0d924941ac0b534c4af79b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdJEp49w0+DC2g+VcHWBJsBE7Bm6NZSmx5dP/uPwSEfnmLD4/DvKTD+gxweAyY5CaPnJej4SBx/jkLPCFYrHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:21:27.765198Z","bundle_sha256":"06e56e1f56d989350d188a8bcf71bbe139ea2d7fb325d06630553c8354d780ac"}}