{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5EELCDC3GYLO6DURGWD2HWML3B","short_pith_number":"pith:5EELCDC3","canonical_record":{"source":{"id":"1605.05163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-17T13:44:14Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a8adf236cb4e54ca96b234933817ea7ed844c62b382b20ae34424857e37d463f","abstract_canon_sha256":"387fba4531ad177b093dc7d9804c0078db77be5d40cf07bb408e154bfceec3f4"},"schema_version":"1.0"},"canonical_sha256":"e908b10c5b3616ef0e913587a3d98bd84d52cf6e24645ba50f040393c16687a8","source":{"kind":"arxiv","id":"1605.05163","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05163","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05163v1","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05163","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"5EELCDC3GYLO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5EELCDC3GYLO6DUR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5EELCDC3","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5EELCDC3GYLO6DURGWD2HWML3B","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-17T13:44:14Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"a8adf236cb4e54ca96b234933817ea7ed844c62b382b20ae34424857e37d463f","abstract_canon_sha256":"387fba4531ad177b093dc7d9804c0078db77be5d40cf07bb408e154bfceec3f4"},"schema_version":"1.0"},"canonical_sha256":"e908b10c5b3616ef0e913587a3d98bd84d52cf6e24645ba50f040393c16687a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:37.201077Z","signature_b64":"VYE1pUUvjfIf789lCVVR9HHj8NhgPCmmuDqSO8PRRwvzzjqpQKo0Rjvmrt/OwImnQqzHgixt7WY+PCythU7/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e908b10c5b3616ef0e913587a3d98bd84d52cf6e24645ba50f040393c16687a8","last_reissued_at":"2026-05-18T01:14:37.200352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:37.200352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05163","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":"2026-05-18T01:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2E8XeMBd2WHVWmmd4CSdt3+hUu9ZSv6jeSUkn1L3kih/o7gzqO3hWICRf4MgpWVpkQ2yHp1X7h+4QDB2d2dnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:31:25.322067Z"},"content_sha256":"ad576b2757294365a6a6ad165eaa96638bb84fbfddb012a558bf127e29c724c5","schema_version":"1.0","event_id":"sha256:ad576b2757294365a6a6ad165eaa96638bb84fbfddb012a558bf127e29c724c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5EELCDC3GYLO6DURGWD2HWML3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Character varieties and actions on products of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"David Fisher, Matthew Stover, Michael Larsen, Ralf Spatzier","submitted_at":"2016-05-17T13:44:14Z","abstract_excerpt":"It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence trees. We provide some obstructions and an arithmetic criterion for existence. The bulk of the paper is devoted to an approach to verifying the arithmetic criterion by studying the character variety of certain surface groups over fields of positive characteristic. The methods may be useful for attempting to determine when groups admit good linear representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05163","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":"2026-05-18T01:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wApTOvC8cx8A0BGUuLnSZdpQIhzNXIRtSf1a7td+6lTtdHwRvt7C/bGo/BjhcAGLXa7QkVVi4phCNvZN1gCPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:31:25.322427Z"},"content_sha256":"7346cfabcc733318208918d423a71415eca09a01f52989c635ce46171bcb80ba","schema_version":"1.0","event_id":"sha256:7346cfabcc733318208918d423a71415eca09a01f52989c635ce46171bcb80ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5EELCDC3GYLO6DURGWD2HWML3B/bundle.json","state_url":"https://pith.science/pith/5EELCDC3GYLO6DURGWD2HWML3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5EELCDC3GYLO6DURGWD2HWML3B/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":"2026-05-30T07:31:25Z","links":{"resolver":"https://pith.science/pith/5EELCDC3GYLO6DURGWD2HWML3B","bundle":"https://pith.science/pith/5EELCDC3GYLO6DURGWD2HWML3B/bundle.json","state":"https://pith.science/pith/5EELCDC3GYLO6DURGWD2HWML3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5EELCDC3GYLO6DURGWD2HWML3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5EELCDC3GYLO6DURGWD2HWML3B","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":"387fba4531ad177b093dc7d9804c0078db77be5d40cf07bb408e154bfceec3f4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-17T13:44:14Z","title_canon_sha256":"a8adf236cb4e54ca96b234933817ea7ed844c62b382b20ae34424857e37d463f"},"schema_version":"1.0","source":{"id":"1605.05163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05163","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05163v1","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05163","created_at":"2026-05-18T01:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"5EELCDC3GYLO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5EELCDC3GYLO6DUR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5EELCDC3","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:7346cfabcc733318208918d423a71415eca09a01f52989c635ce46171bcb80ba","target":"graph","created_at":"2026-05-18T01:14:37Z","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":"It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a free and proper action on a finite product of bounded valence trees. We provide some obstructions and an arithmetic criterion for existence. The bulk of the paper is devoted to an approach to verifying the arithmetic criterion by studying the character variety of certain surface groups over fields of positive characteristic. The methods may be useful for attempting to determine when groups admit good linear representati","authors_text":"David Fisher, Matthew Stover, Michael Larsen, Ralf Spatzier","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-17T13:44:14Z","title":"Character varieties and actions on products of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05163","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:ad576b2757294365a6a6ad165eaa96638bb84fbfddb012a558bf127e29c724c5","target":"record","created_at":"2026-05-18T01:14:37Z","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":"387fba4531ad177b093dc7d9804c0078db77be5d40cf07bb408e154bfceec3f4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-17T13:44:14Z","title_canon_sha256":"a8adf236cb4e54ca96b234933817ea7ed844c62b382b20ae34424857e37d463f"},"schema_version":"1.0","source":{"id":"1605.05163","kind":"arxiv","version":1}},"canonical_sha256":"e908b10c5b3616ef0e913587a3d98bd84d52cf6e24645ba50f040393c16687a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e908b10c5b3616ef0e913587a3d98bd84d52cf6e24645ba50f040393c16687a8","first_computed_at":"2026-05-18T01:14:37.200352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:37.200352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VYE1pUUvjfIf789lCVVR9HHj8NhgPCmmuDqSO8PRRwvzzjqpQKo0Rjvmrt/OwImnQqzHgixt7WY+PCythU7/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:37.201077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad576b2757294365a6a6ad165eaa96638bb84fbfddb012a558bf127e29c724c5","sha256:7346cfabcc733318208918d423a71415eca09a01f52989c635ce46171bcb80ba"],"state_sha256":"b5e1f153d36f762d9f4bfbfd4f22d1925a6240232d93f3c026689546957c2e23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8EgLLPrdg5IlZ0gARTyUWIDVAXifGe6WOuCG8NIBZl1dP9CIeAZf9DpQfLnOcB3K2C6E4Ebm4doPfZaTm4iBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:31:25.324660Z","bundle_sha256":"012138d158369c7c5e4f21bf3d780114e6aea18c4d0a7eb37726152e4d34ab07"}}