{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LOFPV57HUNQ6FK3TOH3N6NQNFD","short_pith_number":"pith:LOFPV57H","canonical_record":{"source":{"id":"1306.5036","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-21T02:49:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2dfeabc3d0ac443701239fdb2b8dfa2592e330cce0e7cbee882a1c9140304515","abstract_canon_sha256":"434947228f55f66c9be49e3abf69502e84a9751bcdf2ef10d2f28493fe02ede3"},"schema_version":"1.0"},"canonical_sha256":"5b8afaf7e7a361e2ab7371f6df360d28ebf58a1496577751bfac2d7e46eb8aa3","source":{"kind":"arxiv","id":"1306.5036","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5036","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5036v2","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5036","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"LOFPV57HUNQ6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOFPV57HUNQ6FK3T","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOFPV57H","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LOFPV57HUNQ6FK3TOH3N6NQNFD","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5036","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-21T02:49:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2dfeabc3d0ac443701239fdb2b8dfa2592e330cce0e7cbee882a1c9140304515","abstract_canon_sha256":"434947228f55f66c9be49e3abf69502e84a9751bcdf2ef10d2f28493fe02ede3"},"schema_version":"1.0"},"canonical_sha256":"5b8afaf7e7a361e2ab7371f6df360d28ebf58a1496577751bfac2d7e46eb8aa3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:46.953684Z","signature_b64":"DIVmWvLsA/u+z7zD5MTaOvl4hg5ZBdrZKqBJeAJpcdoRB0UzcE/uCul65RiUVqY/AMHujjUEHhjbW3vcjk9tBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b8afaf7e7a361e2ab7371f6df360d28ebf58a1496577751bfac2d7e46eb8aa3","last_reissued_at":"2026-05-18T02:48:46.952993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:46.952993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5036","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":"2026-05-18T02:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PE6Y0IDWz3eJwwGQK8zNbUyErm4JZNauACL7FwkqjTwEg0ck8cS8+yVcN5ojrUN+1lpB9LSiqpY1QD14mP9hBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:38:25.640681Z"},"content_sha256":"5b964f8b1a6106f877e02416b915bec0591386d53cc23cfce1bf77d97fcc089c","schema_version":"1.0","event_id":"sha256:5b964f8b1a6106f877e02416b915bec0591386d53cc23cfce1bf77d97fcc089c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LOFPV57HUNQ6FK3TOH3N6NQNFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inertia groups of a toric DM stack, fake weighted projective spaces, and labelled sheared simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"David Johannsen, Derek Krepski, Megumi Harada, Rebecca Goldin","submitted_at":"2013-06-21T02:49:54Z","abstract_excerpt":"This paper determines the inertia groups (isotropy groups) of the points of a toric Deligne-Mumford stack [Z/G] (considered over the category of smooth manifolds) that is realized from a quotient construction using a stacky fan or stacky polytope. The computation provides an explicit correspondence between certain geometric and combinatorial data. In particular, we obtain a computation of the connected component of the identity element $G_0 \\subset G$ and the component group $G/G_0$ in terms of the underlying stacky fan, enabling us to characterize the toric DM stacks which are global quotient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5036","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":"2026-05-18T02:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDAY9iMrGubKddaDgZ+ruu/FnmCNz4i4AGMtXyWUD4Qn2mDC2zaz0nCQkZ3Cqpa0oO6tG+0/GUVEuPUaoPCTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:38:25.641344Z"},"content_sha256":"854bdede12609751871523e60fb11d0a7052b1c42790f4ee10a21dba82e537c1","schema_version":"1.0","event_id":"sha256:854bdede12609751871523e60fb11d0a7052b1c42790f4ee10a21dba82e537c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD/bundle.json","state_url":"https://pith.science/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD/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":"2026-05-30T21:38:25Z","links":{"resolver":"https://pith.science/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD","bundle":"https://pith.science/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD/bundle.json","state":"https://pith.science/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOFPV57HUNQ6FK3TOH3N6NQNFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LOFPV57HUNQ6FK3TOH3N6NQNFD","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":"434947228f55f66c9be49e3abf69502e84a9751bcdf2ef10d2f28493fe02ede3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-21T02:49:54Z","title_canon_sha256":"2dfeabc3d0ac443701239fdb2b8dfa2592e330cce0e7cbee882a1c9140304515"},"schema_version":"1.0","source":{"id":"1306.5036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5036","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5036v2","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5036","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"LOFPV57HUNQ6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOFPV57HUNQ6FK3T","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOFPV57H","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:854bdede12609751871523e60fb11d0a7052b1c42790f4ee10a21dba82e537c1","target":"graph","created_at":"2026-05-18T02:48:46Z","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":"This paper determines the inertia groups (isotropy groups) of the points of a toric Deligne-Mumford stack [Z/G] (considered over the category of smooth manifolds) that is realized from a quotient construction using a stacky fan or stacky polytope. The computation provides an explicit correspondence between certain geometric and combinatorial data. In particular, we obtain a computation of the connected component of the identity element $G_0 \\subset G$ and the component group $G/G_0$ in terms of the underlying stacky fan, enabling us to characterize the toric DM stacks which are global quotient","authors_text":"David Johannsen, Derek Krepski, Megumi Harada, Rebecca Goldin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-21T02:49:54Z","title":"Inertia groups of a toric DM stack, fake weighted projective spaces, and labelled sheared simplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5036","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":"sha256:5b964f8b1a6106f877e02416b915bec0591386d53cc23cfce1bf77d97fcc089c","target":"record","created_at":"2026-05-18T02:48:46Z","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":"434947228f55f66c9be49e3abf69502e84a9751bcdf2ef10d2f28493fe02ede3","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-21T02:49:54Z","title_canon_sha256":"2dfeabc3d0ac443701239fdb2b8dfa2592e330cce0e7cbee882a1c9140304515"},"schema_version":"1.0","source":{"id":"1306.5036","kind":"arxiv","version":2}},"canonical_sha256":"5b8afaf7e7a361e2ab7371f6df360d28ebf58a1496577751bfac2d7e46eb8aa3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b8afaf7e7a361e2ab7371f6df360d28ebf58a1496577751bfac2d7e46eb8aa3","first_computed_at":"2026-05-18T02:48:46.952993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:46.952993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DIVmWvLsA/u+z7zD5MTaOvl4hg5ZBdrZKqBJeAJpcdoRB0UzcE/uCul65RiUVqY/AMHujjUEHhjbW3vcjk9tBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:46.953684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b964f8b1a6106f877e02416b915bec0591386d53cc23cfce1bf77d97fcc089c","sha256:854bdede12609751871523e60fb11d0a7052b1c42790f4ee10a21dba82e537c1"],"state_sha256":"16f133e32b6137c70a05db39f8b2ede42de6a342e0ce383da32a6ff23103d6c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/S86FpYsnoWnJ/KBaL/+IjsPtBUcFJePEKuUYmJRVsNlht8FbnEBelf2TgXy7JJtdW9Xx3MUrqMToRI58MWpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:38:25.644836Z","bundle_sha256":"0ecd86eb610564aa9d65292729ba85dad82274adc34021ff18fab13d1a56e58b"}}