{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HRTUENMDB3PQQ32CLVBYEXXQBU","short_pith_number":"pith:HRTUENMD","canonical_record":{"source":{"id":"1709.09026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-09-26T14:10:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"59b4d6e140106a065170147600fdf3bf20f8e0ad865b217d0c38535fe5856a31","abstract_canon_sha256":"062a6f64c9d9cb5ee652c5e03d9eb9436761a6d7f0749ee7a8bb9b06bc50896d"},"schema_version":"1.0"},"canonical_sha256":"3c674235830edf086f425d43825ef00d1e48fd018896678e54d4ad9e9f7f566f","source":{"kind":"arxiv","id":"1709.09026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09026","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09026v1","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09026","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"pith_short_12","alias_value":"HRTUENMDB3PQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HRTUENMDB3PQQ32C","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HRTUENMD","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HRTUENMDB3PQQ32CLVBYEXXQBU","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-09-26T14:10:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"59b4d6e140106a065170147600fdf3bf20f8e0ad865b217d0c38535fe5856a31","abstract_canon_sha256":"062a6f64c9d9cb5ee652c5e03d9eb9436761a6d7f0749ee7a8bb9b06bc50896d"},"schema_version":"1.0"},"canonical_sha256":"3c674235830edf086f425d43825ef00d1e48fd018896678e54d4ad9e9f7f566f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:21.343489Z","signature_b64":"IDC2vgb0MWChWkBW5ev3gM4ST4nILA6eJiRpO6UpeHQpj8SJlTI2oSxlfED8ISmnVAE5GO38QFgsU9r4vLaEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c674235830edf086f425d43825ef00d1e48fd018896678e54d4ad9e9f7f566f","last_reissued_at":"2026-05-18T00:34:21.343071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:21.343071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09026","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":"2026-05-18T00:34:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Se3YF0UJAx92hIVBDCwbDn1t1fbdtEZIb22PYfRGb4gbHEKsjCK+VcJrhlwJf2MKE0oLMuIX4ZS3s/kwcVetDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:27:28.918805Z"},"content_sha256":"399dc105f88e0bd747d964cd671987de9faeeb2f0e0f6d3be2a3549feebd0610","schema_version":"1.0","event_id":"sha256:399dc105f88e0bd747d964cd671987de9faeeb2f0e0f6d3be2a3549feebd0610"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HRTUENMDB3PQQ32CLVBYEXXQBU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Motions of grid-like reflection frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Bernd Schulze, Derek Kitson","submitted_at":"2017-09-26T14:10:05Z","abstract_excerpt":"Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the reflection acts freely on the vertex set. At the framework level, these characterisations are given in terms of induced monochrome subgraph decompositions, and at the graph level they are given in terms of sparsity counts and recursive construction sequences for the corresponding signed quotient graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09026","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":"2026-05-18T00:34:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NWL+AtRKlNhylXFCzAHahlZnoA6xOG5Fwmh2sJ9semGc1k7bMezc5CxGygE9VZv6k26PfkR96sC92h1mzGxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:27:28.919489Z"},"content_sha256":"c3cad79296ccd45ef830d5d03bef533f5a598632c7c50dab4e5bc49ee41d0b60","schema_version":"1.0","event_id":"sha256:c3cad79296ccd45ef830d5d03bef533f5a598632c7c50dab4e5bc49ee41d0b60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRTUENMDB3PQQ32CLVBYEXXQBU/bundle.json","state_url":"https://pith.science/pith/HRTUENMDB3PQQ32CLVBYEXXQBU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRTUENMDB3PQQ32CLVBYEXXQBU/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":"2026-05-26T13:27:28Z","links":{"resolver":"https://pith.science/pith/HRTUENMDB3PQQ32CLVBYEXXQBU","bundle":"https://pith.science/pith/HRTUENMDB3PQQ32CLVBYEXXQBU/bundle.json","state":"https://pith.science/pith/HRTUENMDB3PQQ32CLVBYEXXQBU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRTUENMDB3PQQ32CLVBYEXXQBU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HRTUENMDB3PQQ32CLVBYEXXQBU","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":"062a6f64c9d9cb5ee652c5e03d9eb9436761a6d7f0749ee7a8bb9b06bc50896d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-09-26T14:10:05Z","title_canon_sha256":"59b4d6e140106a065170147600fdf3bf20f8e0ad865b217d0c38535fe5856a31"},"schema_version":"1.0","source":{"id":"1709.09026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09026","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09026v1","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09026","created_at":"2026-05-18T00:34:21Z"},{"alias_kind":"pith_short_12","alias_value":"HRTUENMDB3PQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HRTUENMDB3PQQ32C","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HRTUENMD","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:c3cad79296ccd45ef830d5d03bef533f5a598632c7c50dab4e5bc49ee41d0b60","target":"graph","created_at":"2026-05-18T00:34:21Z","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"},"paper":{"abstract_excerpt":"Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the reflection acts freely on the vertex set. At the framework level, these characterisations are given in terms of induced monochrome subgraph decompositions, and at the graph level they are given in terms of sparsity counts and recursive construction sequences for the corresponding signed quotient graphs.","authors_text":"Bernd Schulze, Derek Kitson","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-09-26T14:10:05Z","title":"Motions of grid-like reflection frameworks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09026","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":"sha256:399dc105f88e0bd747d964cd671987de9faeeb2f0e0f6d3be2a3549feebd0610","target":"record","created_at":"2026-05-18T00:34:21Z","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":"062a6f64c9d9cb5ee652c5e03d9eb9436761a6d7f0749ee7a8bb9b06bc50896d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-09-26T14:10:05Z","title_canon_sha256":"59b4d6e140106a065170147600fdf3bf20f8e0ad865b217d0c38535fe5856a31"},"schema_version":"1.0","source":{"id":"1709.09026","kind":"arxiv","version":1}},"canonical_sha256":"3c674235830edf086f425d43825ef00d1e48fd018896678e54d4ad9e9f7f566f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c674235830edf086f425d43825ef00d1e48fd018896678e54d4ad9e9f7f566f","first_computed_at":"2026-05-18T00:34:21.343071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:21.343071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IDC2vgb0MWChWkBW5ev3gM4ST4nILA6eJiRpO6UpeHQpj8SJlTI2oSxlfED8ISmnVAE5GO38QFgsU9r4vLaEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:21.343489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:399dc105f88e0bd747d964cd671987de9faeeb2f0e0f6d3be2a3549feebd0610","sha256:c3cad79296ccd45ef830d5d03bef533f5a598632c7c50dab4e5bc49ee41d0b60"],"state_sha256":"4beffe6e79bbea84e972599ec9bebbdd7a9dd5df80441b8a900dbdbe8f4d6dad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iYb83S2vcXnLh/X92RfKHF9DdVhq8ZWQVz9NcOOI+GSJ8GPENNdYI6jXLYYdydAdgUw1eEVIalMwHqttBLDtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:27:28.923092Z","bundle_sha256":"073f15f6dcabaca77c78bfa9f96e4b7a291d94967f9d93286e1f3a7eef165a16"}}