{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FMI4RLMFQ57MEN7BKBTGJMJBX5","short_pith_number":"pith:FMI4RLMF","canonical_record":{"source":{"id":"1711.09610","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-27T10:20:22Z","cross_cats_sorted":[],"title_canon_sha256":"9404063c5b96bc500104240821e886e4cafb151da7272dbd197bc8576cd7f2e5","abstract_canon_sha256":"8f4f3aa96bcc72f437ba0c5aade17a19935aa5aad7c48d94c041c51f6769a898"},"schema_version":"1.0"},"canonical_sha256":"2b11c8ad85877ec237e1506664b121bf444fe6e8dbfa4c523029b2df27a0f591","source":{"kind":"arxiv","id":"1711.09610","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09610","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09610v2","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09610","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"FMI4RLMFQ57M","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FMI4RLMFQ57MEN7B","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FMI4RLMF","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FMI4RLMFQ57MEN7BKBTGJMJBX5","target":"record","payload":{"canonical_record":{"source":{"id":"1711.09610","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-27T10:20:22Z","cross_cats_sorted":[],"title_canon_sha256":"9404063c5b96bc500104240821e886e4cafb151da7272dbd197bc8576cd7f2e5","abstract_canon_sha256":"8f4f3aa96bcc72f437ba0c5aade17a19935aa5aad7c48d94c041c51f6769a898"},"schema_version":"1.0"},"canonical_sha256":"2b11c8ad85877ec237e1506664b121bf444fe6e8dbfa4c523029b2df27a0f591","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:41.614481Z","signature_b64":"5AWCdEPCfdBBR7VPFLNe4kK8Q4xRMU1I8pL1cJUVMWxU7D6kLCnCWGbtQcL8TXO+SX6sMyx9WTg3COM4fPK8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b11c8ad85877ec237e1506664b121bf444fe6e8dbfa4c523029b2df27a0f591","last_reissued_at":"2026-05-18T00:03:41.614073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:41.614073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.09610","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":"2026-05-18T00:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nh9+b2tESLsADnKFHGcsrWDEIeCX5FKZa2rJT5mKBz9DlGjpmOx7W6FssaClM/ryKX3/x3VWPt8hGwSeohDrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:24:38.857136Z"},"content_sha256":"4e07bef27bb62c8d178ee3c6654dcc965e3ebdbae66a938d59386a3405354c71","schema_version":"1.0","event_id":"sha256:4e07bef27bb62c8d178ee3c6654dcc965e3ebdbae66a938d59386a3405354c71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FMI4RLMFQ57MEN7BKBTGJMJBX5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Willis Theory via Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Stephan Tornier, Timothy P. Bywaters","submitted_at":"2017-11-27T10:20:22Z","abstract_excerpt":"We study the scale and tidy subgroups of an endomorphism of a totally disconnected locally compact group using a geometric framework. This leads to new interpretations of tidy subgroups and the scale function. Foremost, we obtain a geometric tidying procedure which applies to endomorphisms as well as a geometric proof of the fact that tidiness is equivalent to being minimizing for a given endomorphism. Our framework also yields an endomorphism version of the Baumgartner-Willis tree representation theorem. We conclude with a construction of new endomorphisms of totally disconnected locally comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09610","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":"2026-05-18T00:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l42sf8WhSg4S0D6RttNYSIcWTPi0YKp6CVKuNZgOscPJGPpNuZvoAwAvnhUG3mSWUw1FUM3UmhSrT8OnFxqJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:24:38.857771Z"},"content_sha256":"748c759a68ac2199f640e4b47c28b0e6183d2ad7a1ac421fade25f5a3665a3e6","schema_version":"1.0","event_id":"sha256:748c759a68ac2199f640e4b47c28b0e6183d2ad7a1ac421fade25f5a3665a3e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5/bundle.json","state_url":"https://pith.science/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5/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":"2026-05-27T21:24:38Z","links":{"resolver":"https://pith.science/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5","bundle":"https://pith.science/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5/bundle.json","state":"https://pith.science/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMI4RLMFQ57MEN7BKBTGJMJBX5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FMI4RLMFQ57MEN7BKBTGJMJBX5","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":"8f4f3aa96bcc72f437ba0c5aade17a19935aa5aad7c48d94c041c51f6769a898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-27T10:20:22Z","title_canon_sha256":"9404063c5b96bc500104240821e886e4cafb151da7272dbd197bc8576cd7f2e5"},"schema_version":"1.0","source":{"id":"1711.09610","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09610","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09610v2","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09610","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"FMI4RLMFQ57M","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FMI4RLMFQ57MEN7B","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FMI4RLMF","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:748c759a68ac2199f640e4b47c28b0e6183d2ad7a1ac421fade25f5a3665a3e6","target":"graph","created_at":"2026-05-18T00:03:41Z","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 study the scale and tidy subgroups of an endomorphism of a totally disconnected locally compact group using a geometric framework. This leads to new interpretations of tidy subgroups and the scale function. Foremost, we obtain a geometric tidying procedure which applies to endomorphisms as well as a geometric proof of the fact that tidiness is equivalent to being minimizing for a given endomorphism. Our framework also yields an endomorphism version of the Baumgartner-Willis tree representation theorem. We conclude with a construction of new endomorphisms of totally disconnected locally comp","authors_text":"Stephan Tornier, Timothy P. Bywaters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-27T10:20:22Z","title":"Willis Theory via Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09610","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":"sha256:4e07bef27bb62c8d178ee3c6654dcc965e3ebdbae66a938d59386a3405354c71","target":"record","created_at":"2026-05-18T00:03:41Z","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":"8f4f3aa96bcc72f437ba0c5aade17a19935aa5aad7c48d94c041c51f6769a898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-27T10:20:22Z","title_canon_sha256":"9404063c5b96bc500104240821e886e4cafb151da7272dbd197bc8576cd7f2e5"},"schema_version":"1.0","source":{"id":"1711.09610","kind":"arxiv","version":2}},"canonical_sha256":"2b11c8ad85877ec237e1506664b121bf444fe6e8dbfa4c523029b2df27a0f591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b11c8ad85877ec237e1506664b121bf444fe6e8dbfa4c523029b2df27a0f591","first_computed_at":"2026-05-18T00:03:41.614073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:41.614073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5AWCdEPCfdBBR7VPFLNe4kK8Q4xRMU1I8pL1cJUVMWxU7D6kLCnCWGbtQcL8TXO+SX6sMyx9WTg3COM4fPK8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:41.614481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09610","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e07bef27bb62c8d178ee3c6654dcc965e3ebdbae66a938d59386a3405354c71","sha256:748c759a68ac2199f640e4b47c28b0e6183d2ad7a1ac421fade25f5a3665a3e6"],"state_sha256":"63e52638c92fc0f3f730d9969c6da71f6f97e10e47eacf518ba1df7d07def71f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f5jMz2nS/FYvD5uJOngxiJaaqpa01JNStCOUPQekFPWOyAnhqQPQpHo39WenazDA6/gpnluJRuJr4oGbXqpVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:24:38.860554Z","bundle_sha256":"e9be8bef11848d8f4d63bac786dfb44aef3f929596222c87c1ef73df1056aea5"}}