{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ATXKYIY7KC3ZXOMOVJ377G73I2","short_pith_number":"pith:ATXKYIY7","canonical_record":{"source":{"id":"1612.06499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-20T03:59:43Z","cross_cats_sorted":[],"title_canon_sha256":"558413b3d9c48c95d27995b2bfca2c44e3e107fa75969e3ab7da58fef2cce76f","abstract_canon_sha256":"8395174ae6fc82326ced72d2ea567e4668bd4f5c1e7c9492e70ae3946b7a5ae2"},"schema_version":"1.0"},"canonical_sha256":"04eeac231f50b79bb98eaa77ff9bfb46ba8e796d044975178123c0e44d973d5e","source":{"kind":"arxiv","id":"1612.06499","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06499","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06499v2","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06499","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"ATXKYIY7KC3Z","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ATXKYIY7KC3ZXOMO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ATXKYIY7","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ATXKYIY7KC3ZXOMOVJ377G73I2","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-20T03:59:43Z","cross_cats_sorted":[],"title_canon_sha256":"558413b3d9c48c95d27995b2bfca2c44e3e107fa75969e3ab7da58fef2cce76f","abstract_canon_sha256":"8395174ae6fc82326ced72d2ea567e4668bd4f5c1e7c9492e70ae3946b7a5ae2"},"schema_version":"1.0"},"canonical_sha256":"04eeac231f50b79bb98eaa77ff9bfb46ba8e796d044975178123c0e44d973d5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:15.176309Z","signature_b64":"fwpYDYjH0nQsPOeshq6iJI3GyNCAoLJAlHvun27kd1Ceg4X8J4VGXbeXKPTZcY8GU8zt8DlrSG3NoMCsyZ2UAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04eeac231f50b79bb98eaa77ff9bfb46ba8e796d044975178123c0e44d973d5e","last_reissued_at":"2026-05-18T00:54:15.175890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:15.175890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06499","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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xodyHHWLrdNj8COTA/TKN/WohCjFnwO12hYXM1EZihx0tnzpQQLuywyWo8wunBSwcp+cr8FUcrd87my9bU4JBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:03:12.778983Z"},"content_sha256":"51a434bc746f2899ab8c65470673dfd05e114a76b48ae3eb552dc44f7f8009c0","schema_version":"1.0","event_id":"sha256:51a434bc746f2899ab8c65470673dfd05e114a76b48ae3eb552dc44f7f8009c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ATXKYIY7KC3ZXOMOVJ377G73I2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariable generation of certain groups of piecewise linear homeomorphisms of the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Shigenori Matsumoto, Yoshifumi Matsuda","submitted_at":"2016-12-20T03:59:43Z","abstract_excerpt":"We show that certain groups of piecewise linear homeomorphims of the interval are invariably generated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06499","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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HnIWZ9kt5Z94YfkHJUnP991wvNdjjBC0zrEIPXc2kl3M9Gr2W0jWGsyROlQ76a6Y0nNuoEYfi7vdeVHUX/yeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:03:12.779330Z"},"content_sha256":"b123f089d64a1bf8f0275867633f510b3db4f851d63326f1d850cc92ed6295e1","schema_version":"1.0","event_id":"sha256:b123f089d64a1bf8f0275867633f510b3db4f851d63326f1d850cc92ed6295e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ATXKYIY7KC3ZXOMOVJ377G73I2/bundle.json","state_url":"https://pith.science/pith/ATXKYIY7KC3ZXOMOVJ377G73I2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ATXKYIY7KC3ZXOMOVJ377G73I2/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":"2026-06-24T20:03:12Z","links":{"resolver":"https://pith.science/pith/ATXKYIY7KC3ZXOMOVJ377G73I2","bundle":"https://pith.science/pith/ATXKYIY7KC3ZXOMOVJ377G73I2/bundle.json","state":"https://pith.science/pith/ATXKYIY7KC3ZXOMOVJ377G73I2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ATXKYIY7KC3ZXOMOVJ377G73I2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ATXKYIY7KC3ZXOMOVJ377G73I2","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":"8395174ae6fc82326ced72d2ea567e4668bd4f5c1e7c9492e70ae3946b7a5ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-20T03:59:43Z","title_canon_sha256":"558413b3d9c48c95d27995b2bfca2c44e3e107fa75969e3ab7da58fef2cce76f"},"schema_version":"1.0","source":{"id":"1612.06499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06499","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06499v2","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06499","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"ATXKYIY7KC3Z","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ATXKYIY7KC3ZXOMO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ATXKYIY7","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:b123f089d64a1bf8f0275867633f510b3db4f851d63326f1d850cc92ed6295e1","target":"graph","created_at":"2026-05-18T00:54:15Z","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":"We show that certain groups of piecewise linear homeomorphims of the interval are invariably generated.","authors_text":"Shigenori Matsumoto, Yoshifumi Matsuda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-20T03:59:43Z","title":"Invariable generation of certain groups of piecewise linear homeomorphisms of the interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06499","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":"sha256:51a434bc746f2899ab8c65470673dfd05e114a76b48ae3eb552dc44f7f8009c0","target":"record","created_at":"2026-05-18T00:54:15Z","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":"8395174ae6fc82326ced72d2ea567e4668bd4f5c1e7c9492e70ae3946b7a5ae2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-20T03:59:43Z","title_canon_sha256":"558413b3d9c48c95d27995b2bfca2c44e3e107fa75969e3ab7da58fef2cce76f"},"schema_version":"1.0","source":{"id":"1612.06499","kind":"arxiv","version":2}},"canonical_sha256":"04eeac231f50b79bb98eaa77ff9bfb46ba8e796d044975178123c0e44d973d5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04eeac231f50b79bb98eaa77ff9bfb46ba8e796d044975178123c0e44d973d5e","first_computed_at":"2026-05-18T00:54:15.175890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.175890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwpYDYjH0nQsPOeshq6iJI3GyNCAoLJAlHvun27kd1Ceg4X8J4VGXbeXKPTZcY8GU8zt8DlrSG3NoMCsyZ2UAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.176309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51a434bc746f2899ab8c65470673dfd05e114a76b48ae3eb552dc44f7f8009c0","sha256:b123f089d64a1bf8f0275867633f510b3db4f851d63326f1d850cc92ed6295e1"],"state_sha256":"c2b13bfc3470866528416463223f169364b9e22c97600cc4a3307fad99aa0d4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJICEdsZGT7beG+sbuP+o8K5oQsBiCjKpY8VoP0rWB12nKWr0c/jmeH8j/9ShB4cvvowi/8d+bHsBhpCICs1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:03:12.781828Z","bundle_sha256":"df2582f3ae43e7fa30acf63d052a67316eb699a2cedd9079259d28776e51670a"}}