{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PKH3T4KD5AKY45EZKRTJCH4TFS","short_pith_number":"pith:PKH3T4KD","canonical_record":{"source":{"id":"1802.07085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-20T12:36:44Z","cross_cats_sorted":["cs.CC","cs.FL"],"title_canon_sha256":"0133305ed7e129583813aaccdc5f3329a2ca915f4bc63df20badf33742421c75","abstract_canon_sha256":"9d9b57ac8783eb3d2b1d834fb86712f21c3f8b877acc3dad517953ba9ad01da3"},"schema_version":"1.0"},"canonical_sha256":"7a8fb9f143e8158e74995466911f932c8d30e018b5ed245119b5bf7d4e6acc38","source":{"kind":"arxiv","id":"1802.07085","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07085","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07085v1","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07085","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"PKH3T4KD5AKY","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PKH3T4KD5AKY45EZ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PKH3T4KD","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PKH3T4KD5AKY45EZKRTJCH4TFS","target":"record","payload":{"canonical_record":{"source":{"id":"1802.07085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-20T12:36:44Z","cross_cats_sorted":["cs.CC","cs.FL"],"title_canon_sha256":"0133305ed7e129583813aaccdc5f3329a2ca915f4bc63df20badf33742421c75","abstract_canon_sha256":"9d9b57ac8783eb3d2b1d834fb86712f21c3f8b877acc3dad517953ba9ad01da3"},"schema_version":"1.0"},"canonical_sha256":"7a8fb9f143e8158e74995466911f932c8d30e018b5ed245119b5bf7d4e6acc38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:53.591616Z","signature_b64":"DW4lU7l1LOh+vEY2oZbxvn9Z4y+5TYHHqzxMi3V/CjCEj9MriWHnYZFbyuOVlf5Upt+fG9OXDttbbfTDXVXkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a8fb9f143e8158e74995466911f932c8d30e018b5ed245119b5bf7d4e6acc38","last_reissued_at":"2026-05-18T00:22:53.591241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:53.591241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.07085","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":"2026-05-18T00:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+tyO3Qno9YOADZm8Wik49QWhkeiD4m8i9r3xKcRraLLaSNaR8laOzakLKCf4M2mIO8Bzndspci/4m8GOGXPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:52:49.424475Z"},"content_sha256":"f1c43d694a1e314e482cd28f91e1215fe851d535e6c04f0d23fc1ff931886a1e","schema_version":"1.0","event_id":"sha256:f1c43d694a1e314e482cd28f91e1215fe851d535e6c04f0d23fc1ff931886a1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PKH3T4KD5AKY45EZKRTJCH4TFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The isomorphism problem for finite extensions of free groups is in PSPACE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.FL"],"primary_cat":"math.GR","authors_text":"Armin Wei{\\ss}, G\\'eraud S\\'enizergues","submitted_at":"2018-02-20T12:36:44Z","abstract_excerpt":"We present an algorithm for the following problem: given a context-free grammar for the word problem of a virtually free group $G$, compute a finite graph of groups $\\mathcal{G}$ with finite vertex groups and fundamental group $G$. Our algorithm is non-deterministic and runs in doubly exponential time. It follows that the isomorphism problem of context-free groups can be solved in doubly exponential space.\n  Moreover, if, instead of a grammar, a finite extension of a free group is given as input, the construction of the graph of groups is in NP and, consequently, the isomorphism problem in PSP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07085","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":"2026-05-18T00:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9wAJ6B38OQql+uYdYjTd4QG6hVzCIoxS5a7RgDNZeoqdbHaH133AUuXAL5Ei6zx+6IvVLNIui/DqWMuY3g7bBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T05:52:49.425234Z"},"content_sha256":"3ef91f3d690377456fb5e3c485f08fcb7b203c5a13ee756623e66275d22d1e22","schema_version":"1.0","event_id":"sha256:3ef91f3d690377456fb5e3c485f08fcb7b203c5a13ee756623e66275d22d1e22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKH3T4KD5AKY45EZKRTJCH4TFS/bundle.json","state_url":"https://pith.science/pith/PKH3T4KD5AKY45EZKRTJCH4TFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKH3T4KD5AKY45EZKRTJCH4TFS/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":"2026-06-06T05:52:49Z","links":{"resolver":"https://pith.science/pith/PKH3T4KD5AKY45EZKRTJCH4TFS","bundle":"https://pith.science/pith/PKH3T4KD5AKY45EZKRTJCH4TFS/bundle.json","state":"https://pith.science/pith/PKH3T4KD5AKY45EZKRTJCH4TFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKH3T4KD5AKY45EZKRTJCH4TFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PKH3T4KD5AKY45EZKRTJCH4TFS","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":"9d9b57ac8783eb3d2b1d834fb86712f21c3f8b877acc3dad517953ba9ad01da3","cross_cats_sorted":["cs.CC","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-20T12:36:44Z","title_canon_sha256":"0133305ed7e129583813aaccdc5f3329a2ca915f4bc63df20badf33742421c75"},"schema_version":"1.0","source":{"id":"1802.07085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07085","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07085v1","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07085","created_at":"2026-05-18T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"PKH3T4KD5AKY","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PKH3T4KD5AKY45EZ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PKH3T4KD","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:3ef91f3d690377456fb5e3c485f08fcb7b203c5a13ee756623e66275d22d1e22","target":"graph","created_at":"2026-05-18T00:22:53Z","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 present an algorithm for the following problem: given a context-free grammar for the word problem of a virtually free group $G$, compute a finite graph of groups $\\mathcal{G}$ with finite vertex groups and fundamental group $G$. Our algorithm is non-deterministic and runs in doubly exponential time. It follows that the isomorphism problem of context-free groups can be solved in doubly exponential space.\n  Moreover, if, instead of a grammar, a finite extension of a free group is given as input, the construction of the graph of groups is in NP and, consequently, the isomorphism problem in PSP","authors_text":"Armin Wei{\\ss}, G\\'eraud S\\'enizergues","cross_cats":["cs.CC","cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-20T12:36:44Z","title":"The isomorphism problem for finite extensions of free groups is in PSPACE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07085","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:f1c43d694a1e314e482cd28f91e1215fe851d535e6c04f0d23fc1ff931886a1e","target":"record","created_at":"2026-05-18T00:22:53Z","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":"9d9b57ac8783eb3d2b1d834fb86712f21c3f8b877acc3dad517953ba9ad01da3","cross_cats_sorted":["cs.CC","cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-20T12:36:44Z","title_canon_sha256":"0133305ed7e129583813aaccdc5f3329a2ca915f4bc63df20badf33742421c75"},"schema_version":"1.0","source":{"id":"1802.07085","kind":"arxiv","version":1}},"canonical_sha256":"7a8fb9f143e8158e74995466911f932c8d30e018b5ed245119b5bf7d4e6acc38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a8fb9f143e8158e74995466911f932c8d30e018b5ed245119b5bf7d4e6acc38","first_computed_at":"2026-05-18T00:22:53.591241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:53.591241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DW4lU7l1LOh+vEY2oZbxvn9Z4y+5TYHHqzxMi3V/CjCEj9MriWHnYZFbyuOVlf5Upt+fG9OXDttbbfTDXVXkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:53.591616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1c43d694a1e314e482cd28f91e1215fe851d535e6c04f0d23fc1ff931886a1e","sha256:3ef91f3d690377456fb5e3c485f08fcb7b203c5a13ee756623e66275d22d1e22"],"state_sha256":"b1c5631e86041aeda7c59aa7cb58579dda72d02fdf19691efe25eebb25910b06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wTLbSs2c/tO0wVMEKsxYXFNYsjTRNf6We7MINDPkIKxazTyznbCdjTp3SJZQAA5oud88Q6Dg3kgRHq/1erADAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T05:52:49.429719Z","bundle_sha256":"aa349bb44d394c668433e45ea56fc5592eac7462d97746cde657192a2ce68d3d"}}