{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:P6B3FGTIATVMBV3CECBTTXSVOW","short_pith_number":"pith:P6B3FGTI","canonical_record":{"source":{"id":"2606.18086","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-16T15:50:13Z","cross_cats_sorted":[],"title_canon_sha256":"46d72e219819a086c141e982eef0c6492fc66c0fa25088c9d540dcd3071f05e9","abstract_canon_sha256":"ed0d6ac066f15f7a52fc8631faa2317579e4171900b5c4bff6c0f91e7b6e9af4"},"schema_version":"1.0"},"canonical_sha256":"7f83b29a6804eac0d762208339de5575bbdf092f975b885bfce6b7f8870636ed","source":{"kind":"arxiv","id":"2606.18086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18086","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18086v1","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18086","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"P6B3FGTIATVM","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_16","alias_value":"P6B3FGTIATVMBV3C","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_8","alias_value":"P6B3FGTI","created_at":"2026-06-19T16:10:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:P6B3FGTIATVMBV3CECBTTXSVOW","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18086","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-16T15:50:13Z","cross_cats_sorted":[],"title_canon_sha256":"46d72e219819a086c141e982eef0c6492fc66c0fa25088c9d540dcd3071f05e9","abstract_canon_sha256":"ed0d6ac066f15f7a52fc8631faa2317579e4171900b5c4bff6c0f91e7b6e9af4"},"schema_version":"1.0"},"canonical_sha256":"7f83b29a6804eac0d762208339de5575bbdf092f975b885bfce6b7f8870636ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:48.166023Z","signature_b64":"uIT4afBNeJ847RlwthSsPo4cpIloPu6gTvk2j5S/jCqtksiym0KOSYms1gGrEZs/3MVVIsP0KRNLA+33l+dfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f83b29a6804eac0d762208339de5575bbdf092f975b885bfce6b7f8870636ed","last_reissued_at":"2026-06-19T16:10:48.165660Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:48.165660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18086","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":"2026-06-19T16:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z9b0M25IvAKBLXhQVB+ssN13wLWp0ZI4wRKV90h+4JRA8cr+GU+RVUGNP9o9tetCameyYDl1H1vCo3IARkkoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:48:30.428006Z"},"content_sha256":"034ffd74de198c92d2e421d4fde102a869575787440836105b4912dfe4bd9977","schema_version":"1.0","event_id":"sha256:034ffd74de198c92d2e421d4fde102a869575787440836105b4912dfe4bd9977"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:P6B3FGTIATVMBV3CECBTTXSVOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Branched Covers of Hyperbolic Groups","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Darius Alizadeh","submitted_at":"2026-06-16T15:50:13Z","abstract_excerpt":"Given a hyperbolic group $G$ and a quasiconvex subgroup $Q$, we define a \\emph{branched cover of $G$ along $g$}, which is a hyperbolic group $H$ with a certain map into $G$. This builds on recent work on drilling hyperbolic groups and generalizes the case where $G$ is the fundamental group of a closed hyperbolic $3$-manifold $M$, $Q \\cong \\mathbb{Z}$ is represented by an embedded geodesic loop $\\gamma$, and $H$ is the fundamental group of a branched cover of $M$ with branching locus $\\gamma$. We show that certain deepness assumptions on Dehn fillings induce branched covers, providing many exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18086","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/2606.18086/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":"2026-06-19T16:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9AXKJLwNePbpANS/dBxciGUQZZCOL9a5pc+mpZn+LbP90Zg/v+fXIam9ysDEggflOVYtrTOYurw/PChNhHreAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:48:30.428433Z"},"content_sha256":"5a05a1a3be5efc52e7b9c3db5eed6e18a7c635f0e8bd44f6c43fc9600d2903e9","schema_version":"1.0","event_id":"sha256:5a05a1a3be5efc52e7b9c3db5eed6e18a7c635f0e8bd44f6c43fc9600d2903e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6B3FGTIATVMBV3CECBTTXSVOW/bundle.json","state_url":"https://pith.science/pith/P6B3FGTIATVMBV3CECBTTXSVOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6B3FGTIATVMBV3CECBTTXSVOW/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":"2026-06-27T03:48:30Z","links":{"resolver":"https://pith.science/pith/P6B3FGTIATVMBV3CECBTTXSVOW","bundle":"https://pith.science/pith/P6B3FGTIATVMBV3CECBTTXSVOW/bundle.json","state":"https://pith.science/pith/P6B3FGTIATVMBV3CECBTTXSVOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6B3FGTIATVMBV3CECBTTXSVOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P6B3FGTIATVMBV3CECBTTXSVOW","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":"ed0d6ac066f15f7a52fc8631faa2317579e4171900b5c4bff6c0f91e7b6e9af4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-16T15:50:13Z","title_canon_sha256":"46d72e219819a086c141e982eef0c6492fc66c0fa25088c9d540dcd3071f05e9"},"schema_version":"1.0","source":{"id":"2606.18086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18086","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18086v1","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18086","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"P6B3FGTIATVM","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_16","alias_value":"P6B3FGTIATVMBV3C","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_8","alias_value":"P6B3FGTI","created_at":"2026-06-19T16:10:48Z"}],"graph_snapshots":[{"event_id":"sha256:5a05a1a3be5efc52e7b9c3db5eed6e18a7c635f0e8bd44f6c43fc9600d2903e9","target":"graph","created_at":"2026-06-19T16:10:48Z","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/2606.18086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a hyperbolic group $G$ and a quasiconvex subgroup $Q$, we define a \\emph{branched cover of $G$ along $g$}, which is a hyperbolic group $H$ with a certain map into $G$. This builds on recent work on drilling hyperbolic groups and generalizes the case where $G$ is the fundamental group of a closed hyperbolic $3$-manifold $M$, $Q \\cong \\mathbb{Z}$ is represented by an embedded geodesic loop $\\gamma$, and $H$ is the fundamental group of a branched cover of $M$ with branching locus $\\gamma$. We show that certain deepness assumptions on Dehn fillings induce branched covers, providing many exam","authors_text":"Darius Alizadeh","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-16T15:50:13Z","title":"Branched Covers of Hyperbolic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18086","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":"sha256:034ffd74de198c92d2e421d4fde102a869575787440836105b4912dfe4bd9977","target":"record","created_at":"2026-06-19T16:10:48Z","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":"ed0d6ac066f15f7a52fc8631faa2317579e4171900b5c4bff6c0f91e7b6e9af4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-16T15:50:13Z","title_canon_sha256":"46d72e219819a086c141e982eef0c6492fc66c0fa25088c9d540dcd3071f05e9"},"schema_version":"1.0","source":{"id":"2606.18086","kind":"arxiv","version":1}},"canonical_sha256":"7f83b29a6804eac0d762208339de5575bbdf092f975b885bfce6b7f8870636ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f83b29a6804eac0d762208339de5575bbdf092f975b885bfce6b7f8870636ed","first_computed_at":"2026-06-19T16:10:48.165660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:48.165660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uIT4afBNeJ847RlwthSsPo4cpIloPu6gTvk2j5S/jCqtksiym0KOSYms1gGrEZs/3MVVIsP0KRNLA+33l+dfAQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:48.166023Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:034ffd74de198c92d2e421d4fde102a869575787440836105b4912dfe4bd9977","sha256:5a05a1a3be5efc52e7b9c3db5eed6e18a7c635f0e8bd44f6c43fc9600d2903e9"],"state_sha256":"93ec547f780224663f1b94af1a6ed889e4b122c5d50c4b2c62504501c3308b2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKucuLytzyjDjPpTtm3VdulvaOQ+2yVXZRaIqGQRtjqaH2tvs/TRqBZyeiMtO1K/d9sEML5FukgdtpO6M5h9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:48:30.430283Z","bundle_sha256":"9619bd6f13d8171cad672a53696a0134e83d2adea6b49db618106261b0529aae"}}