{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LVD5JH2SSTZL22S4Z4NSUZGAB6","short_pith_number":"pith:LVD5JH2S","canonical_record":{"source":{"id":"1104.0968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-05T21:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"eb62632cb5058999df8582cb61fd0d3e9654809a9b54b04c2e39026144e73367","abstract_canon_sha256":"2a0629be15451656465c47f2478a1773009327eb4ea0e30520cd8e8731081a28"},"schema_version":"1.0"},"canonical_sha256":"5d47d49f5294f2bd6a5ccf1b2a64c00f9c700503a10dd11e8d5ad728e96adb65","source":{"kind":"arxiv","id":"1104.0968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0968","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0968v1","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0968","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"LVD5JH2SSTZL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LVD5JH2SSTZL22S4","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LVD5JH2S","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LVD5JH2SSTZL22S4Z4NSUZGAB6","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-05T21:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"eb62632cb5058999df8582cb61fd0d3e9654809a9b54b04c2e39026144e73367","abstract_canon_sha256":"2a0629be15451656465c47f2478a1773009327eb4ea0e30520cd8e8731081a28"},"schema_version":"1.0"},"canonical_sha256":"5d47d49f5294f2bd6a5ccf1b2a64c00f9c700503a10dd11e8d5ad728e96adb65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.226604Z","signature_b64":"+4umSC+lMWdS2xyQ+DFah9GIe3OpwX3Dw3U1VC2rn6owbpc89QEcq2r87o7bwOf/x9e7LKuIl1N/Hr12IPgxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d47d49f5294f2bd6a5ccf1b2a64c00f9c700503a10dd11e8d5ad728e96adb65","last_reissued_at":"2026-05-18T03:02:44.225852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.225852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0968","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":"2026-05-18T03:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R94/ts4+Z2l/tJzknKXo4Wh7COziBr1R+XO7P/a/70XcGRT99xMyLfDJESv/veeSvtOBoHVRERi1+EkejEuWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:34:06.931549Z"},"content_sha256":"19f84381dadcecf9dbb20edc44a4645c414edde7da261af76309d896c43fefed","schema_version":"1.0","event_id":"sha256:19f84381dadcecf9dbb20edc44a4645c414edde7da261af76309d896c43fefed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LVD5JH2SSTZL22S4Z4NSUZGAB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Roots of Dehn twists about separating curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kashyap Rajeevsarathy","submitted_at":"2011-04-05T21:56:11Z","abstract_excerpt":"Let $C$ be a curve in a closed orientable surface $F$ of genus $g \\geq 2$ that separates $F$ into subsurfaces $\\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\\Mod(F)$ of the Dehn twist $t_C$ about $C$. All roots arise from pairs of $C_{n_i}$-actions on the $\\widetilde{F_i}$, where $n=\\lcm(n_1,n_2)$ is the degree of the root, that satisfy a certain compatibility condition. The $C_{n_i}$ actions are of a kind that we call nestled actions, and we classify them using tuples that we call data sets. The compatibility condition can be expressed by a simple formula, al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0968","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":"2026-05-18T03:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IlHQxmU4pHN3zS+Jn3ledHT0D53a9geC3ibBqhCP8/8FV3/pKAMkg7s+zsZ8A0OhrxwmJef746L1d7sJxO1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:34:06.931904Z"},"content_sha256":"447c5332c130979365c590f13a809a5f52e0f38eb83765e06acb68df804cabd1","schema_version":"1.0","event_id":"sha256:447c5332c130979365c590f13a809a5f52e0f38eb83765e06acb68df804cabd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6/bundle.json","state_url":"https://pith.science/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6/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":"2026-06-22T21:34:06Z","links":{"resolver":"https://pith.science/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6","bundle":"https://pith.science/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6/bundle.json","state":"https://pith.science/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVD5JH2SSTZL22S4Z4NSUZGAB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LVD5JH2SSTZL22S4Z4NSUZGAB6","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":"2a0629be15451656465c47f2478a1773009327eb4ea0e30520cd8e8731081a28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-05T21:56:11Z","title_canon_sha256":"eb62632cb5058999df8582cb61fd0d3e9654809a9b54b04c2e39026144e73367"},"schema_version":"1.0","source":{"id":"1104.0968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0968","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0968v1","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0968","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"LVD5JH2SSTZL","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LVD5JH2SSTZL22S4","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LVD5JH2S","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:447c5332c130979365c590f13a809a5f52e0f38eb83765e06acb68df804cabd1","target":"graph","created_at":"2026-05-18T03:02:44Z","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":"Let $C$ be a curve in a closed orientable surface $F$ of genus $g \\geq 2$ that separates $F$ into subsurfaces $\\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\\Mod(F)$ of the Dehn twist $t_C$ about $C$. All roots arise from pairs of $C_{n_i}$-actions on the $\\widetilde{F_i}$, where $n=\\lcm(n_1,n_2)$ is the degree of the root, that satisfy a certain compatibility condition. The $C_{n_i}$ actions are of a kind that we call nestled actions, and we classify them using tuples that we call data sets. The compatibility condition can be expressed by a simple formula, al","authors_text":"Kashyap Rajeevsarathy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-05T21:56:11Z","title":"Roots of Dehn twists about separating curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0968","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":"sha256:19f84381dadcecf9dbb20edc44a4645c414edde7da261af76309d896c43fefed","target":"record","created_at":"2026-05-18T03:02:44Z","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":"2a0629be15451656465c47f2478a1773009327eb4ea0e30520cd8e8731081a28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-04-05T21:56:11Z","title_canon_sha256":"eb62632cb5058999df8582cb61fd0d3e9654809a9b54b04c2e39026144e73367"},"schema_version":"1.0","source":{"id":"1104.0968","kind":"arxiv","version":1}},"canonical_sha256":"5d47d49f5294f2bd6a5ccf1b2a64c00f9c700503a10dd11e8d5ad728e96adb65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d47d49f5294f2bd6a5ccf1b2a64c00f9c700503a10dd11e8d5ad728e96adb65","first_computed_at":"2026-05-18T03:02:44.225852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:44.225852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+4umSC+lMWdS2xyQ+DFah9GIe3OpwX3Dw3U1VC2rn6owbpc89QEcq2r87o7bwOf/x9e7LKuIl1N/Hr12IPgxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:44.226604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19f84381dadcecf9dbb20edc44a4645c414edde7da261af76309d896c43fefed","sha256:447c5332c130979365c590f13a809a5f52e0f38eb83765e06acb68df804cabd1"],"state_sha256":"c83797250915b1c3caeef69782e2d1f567caa294260743da584f870e46a57c3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tj5g5l1s7c3H1OljmEJKs2Q3tG5pYaDvktP//LhQeLQO5cn3zBPObE29AGuRmZTg3CPWDZlQ4YDIY0gSwjsSCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:34:06.933844Z","bundle_sha256":"26b5c0bfdc8bade0efb45883ebae646a8fc997bef4cbad6833f50ebff60c9927"}}