{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:E7PMXJ6ABXRYGAZCQK4HA36PC3","short_pith_number":"pith:E7PMXJ6A","canonical_record":{"source":{"id":"math/0511621","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-11-25T05:29:09Z","cross_cats_sorted":["math.DG","math.DS"],"title_canon_sha256":"8471f71dccc307c818ebfcaba002983df7e5b7092c1ae73cdbe2f77bb71d9886","abstract_canon_sha256":"034d5fbbc8e44838f3c2d56c37daec7c9aa7d7173bbea4742fe107a14a7a7966"},"schema_version":"1.0"},"canonical_sha256":"27decba7c00de383032282b8706fcf16c9e490103090a0633598deba1785ee5b","source":{"kind":"arxiv","id":"math/0511621","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511621","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511621v1","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511621","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"E7PMXJ6ABXRY","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"E7PMXJ6ABXRYGAZC","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"E7PMXJ6A","created_at":"2026-07-04T15:11:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:E7PMXJ6ABXRYGAZCQK4HA36PC3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0511621","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-11-25T05:29:09Z","cross_cats_sorted":["math.DG","math.DS"],"title_canon_sha256":"8471f71dccc307c818ebfcaba002983df7e5b7092c1ae73cdbe2f77bb71d9886","abstract_canon_sha256":"034d5fbbc8e44838f3c2d56c37daec7c9aa7d7173bbea4742fe107a14a7a7966"},"schema_version":"1.0"},"canonical_sha256":"27decba7c00de383032282b8706fcf16c9e490103090a0633598deba1785ee5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:11:45.090928Z","signature_b64":"gQmfbvZgwzbriyQbQJSQNBKe7zlCeO1YLtpC4FVR9Prb8iDXLmL/pFPixD9k92VjyxmO1CudXs3/3tkQqoZdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27decba7c00de383032282b8706fcf16c9e490103090a0633598deba1785ee5b","last_reissued_at":"2026-07-04T15:11:45.090577Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:11:45.090577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0511621","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":"2026-07-04T15:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBk7U6QBg0oXpadoDIxGf1S8+qHyu6wUCVNveZSH77t/m4CkTYjVDVuCyIYiN3QMejCuG/ny9VmuL6zbICMLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T09:15:44.809322Z"},"content_sha256":"80df30839b6cf061039c31bc4ed62c704e332528a4fdabe3cf7c6d999129e8bb","schema_version":"1.0","event_id":"sha256:80df30839b6cf061039c31bc4ed62c704e332528a4fdabe3cf7c6d999129e8bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:E7PMXJ6ABXRYGAZCQK4HA36PC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"End Invariants for $\\SL(2,C)$ characters of the one-holed torus","license":"","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.GT","authors_text":"Ser Peow Tan, Yan Loi Wong, Ying Zhang","submitted_at":"2005-11-25T05:29:09Z","abstract_excerpt":"We define and study the set ${\\mathcal E}(\\rho)$ of end invariants of a $\\SL(2,C)$ character $\\rho$ of the one-holed torus $T$. We show that the set ${\\mathcal E}(\\rho)$ is the entire projective lamination space $\\mathscr{PL}$ of $T$ if and only if (i) $\\rho$ corresponds to the dihedral representation, or (ii) $\\rho$ is real and corresponds to a SU(2) representation; and that otherwise, ${\\mathcal E}(\\rho)$ is closed and has empty interior in $\\mathscr{PL}$. For real characters $\\rho$, we give a complete classification of ${\\mathcal E}(\\rho)$, and show that ${\\mathcal E}(\\rho)$ has either 0, 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511621","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0511621/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrbAnawD9kDBTYVvQFwaBWaUB1FKrjvsXp1NPmu2Vl5B90vRz1i8y7wx7UzSU678U7QLrZQeuDvWLxR8pmSkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T09:15:44.809915Z"},"content_sha256":"7150b94ec6b446df2fbe86ebb95d36658beb74dbe167f6974f41119d5833217e","schema_version":"1.0","event_id":"sha256:7150b94ec6b446df2fbe86ebb95d36658beb74dbe167f6974f41119d5833217e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3/bundle.json","state_url":"https://pith.science/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3/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":"2026-08-23T09:15:44Z","links":{"resolver":"https://pith.science/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3","bundle":"https://pith.science/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3/bundle.json","state":"https://pith.science/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7PMXJ6ABXRYGAZCQK4HA36PC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:E7PMXJ6ABXRYGAZCQK4HA36PC3","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":"034d5fbbc8e44838f3c2d56c37daec7c9aa7d7173bbea4742fe107a14a7a7966","cross_cats_sorted":["math.DG","math.DS"],"license":"","primary_cat":"math.GT","submitted_at":"2005-11-25T05:29:09Z","title_canon_sha256":"8471f71dccc307c818ebfcaba002983df7e5b7092c1ae73cdbe2f77bb71d9886"},"schema_version":"1.0","source":{"id":"math/0511621","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511621","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511621v1","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511621","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"E7PMXJ6ABXRY","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"E7PMXJ6ABXRYGAZC","created_at":"2026-07-04T15:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"E7PMXJ6A","created_at":"2026-07-04T15:11:45Z"}],"graph_snapshots":[{"event_id":"sha256:7150b94ec6b446df2fbe86ebb95d36658beb74dbe167f6974f41119d5833217e","target":"graph","created_at":"2026-07-04T15:11:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0511621/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study the set ${\\mathcal E}(\\rho)$ of end invariants of a $\\SL(2,C)$ character $\\rho$ of the one-holed torus $T$. We show that the set ${\\mathcal E}(\\rho)$ is the entire projective lamination space $\\mathscr{PL}$ of $T$ if and only if (i) $\\rho$ corresponds to the dihedral representation, or (ii) $\\rho$ is real and corresponds to a SU(2) representation; and that otherwise, ${\\mathcal E}(\\rho)$ is closed and has empty interior in $\\mathscr{PL}$. For real characters $\\rho$, we give a complete classification of ${\\mathcal E}(\\rho)$, and show that ${\\mathcal E}(\\rho)$ has either 0, 1","authors_text":"Ser Peow Tan, Yan Loi Wong, Ying Zhang","cross_cats":["math.DG","math.DS"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2005-11-25T05:29:09Z","title":"End Invariants for $\\SL(2,C)$ characters of the one-holed torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511621","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":"sha256:80df30839b6cf061039c31bc4ed62c704e332528a4fdabe3cf7c6d999129e8bb","target":"record","created_at":"2026-07-04T15:11:45Z","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":"034d5fbbc8e44838f3c2d56c37daec7c9aa7d7173bbea4742fe107a14a7a7966","cross_cats_sorted":["math.DG","math.DS"],"license":"","primary_cat":"math.GT","submitted_at":"2005-11-25T05:29:09Z","title_canon_sha256":"8471f71dccc307c818ebfcaba002983df7e5b7092c1ae73cdbe2f77bb71d9886"},"schema_version":"1.0","source":{"id":"math/0511621","kind":"arxiv","version":1}},"canonical_sha256":"27decba7c00de383032282b8706fcf16c9e490103090a0633598deba1785ee5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27decba7c00de383032282b8706fcf16c9e490103090a0633598deba1785ee5b","first_computed_at":"2026-07-04T15:11:45.090577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:11:45.090577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gQmfbvZgwzbriyQbQJSQNBKe7zlCeO1YLtpC4FVR9Prb8iDXLmL/pFPixD9k92VjyxmO1CudXs3/3tkQqoZdAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:11:45.090928Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0511621","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80df30839b6cf061039c31bc4ed62c704e332528a4fdabe3cf7c6d999129e8bb","sha256:7150b94ec6b446df2fbe86ebb95d36658beb74dbe167f6974f41119d5833217e"],"state_sha256":"ebde5f50c33e3acefe69556cb1a182d0291d7033f43cb33b8ecf7a9c64549461"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YorYdXTIYg02dH7Dy7HS0SQ78XFjbPDLhyrPBdfngre0+DUr6ugiuNiRG48WtvrF0M3pU39geY43XLbMDkbnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T09:15:44.814411Z","bundle_sha256":"f5d736d794ccea591042d1dcb9fe3b1378cb5028ac031a7c4f7e5e29c6f4c08a"}}