{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IT7GBGGNF2LGDIR2YQKL5IY5G2","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":"94fc4068e39cf93ba350c6b16a3619c63b228c1d2ef77a7918971536fceb1719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-04T09:03:21Z","title_canon_sha256":"569dc2e53a3e2778e9c89d11bc8e4270dad513fcf58c3ab6881cae47d7e685b6"},"schema_version":"1.0","source":{"id":"1312.1064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1064","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1064v1","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1064","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"IT7GBGGNF2LG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IT7GBGGNF2LGDIR2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IT7GBGGN","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:dc9d8f581a6cc1e40c8ef0f981d7e93b2bee4c860a82e8891be21735c4d672c3","target":"graph","created_at":"2026-05-18T03:05:35Z","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":"A scale-multiplicative semigroup in a totally disconnected, locally compact group $G$ is one for which the restriction of the scale function on $G$ is multiplicative. The maximal scale-multiplicative semigroups in groups acting 2-transitively on the set of ends of trees without leaves are determined in this paper and shown to correspond to geometric features of the tree.","authors_text":"George A. Willis, Jacqui Ramagge, Udo Baumgartner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-04T09:03:21Z","title":"Scale-multiplicative semigroups and geometry: automorphism groups of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1064","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:f44e061dd3f4a5e2e3f58b3a2f6d14085ebb4f434e8cfb511f57018026c0b88b","target":"record","created_at":"2026-05-18T03:05:35Z","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":"94fc4068e39cf93ba350c6b16a3619c63b228c1d2ef77a7918971536fceb1719","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-04T09:03:21Z","title_canon_sha256":"569dc2e53a3e2778e9c89d11bc8e4270dad513fcf58c3ab6881cae47d7e685b6"},"schema_version":"1.0","source":{"id":"1312.1064","kind":"arxiv","version":1}},"canonical_sha256":"44fe6098cd2e9661a23ac414bea31d369631fc1c85e6b24cb5bf1e3fd8ea0bc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44fe6098cd2e9661a23ac414bea31d369631fc1c85e6b24cb5bf1e3fd8ea0bc8","first_computed_at":"2026-05-18T03:05:35.043622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:35.043622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XLSZD9LI7v3vCGkbrijbsINPj5bKrPaCvDRH2Q6toT7XihzHiM5H+PXyN0o8yy/s3zs+t7cb4EYfArvdfvjqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:35.044110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f44e061dd3f4a5e2e3f58b3a2f6d14085ebb4f434e8cfb511f57018026c0b88b","sha256:dc9d8f581a6cc1e40c8ef0f981d7e93b2bee4c860a82e8891be21735c4d672c3"],"state_sha256":"fd499cc07e645709873e5c6bb8b093e0ea4d4ae8e9926625236a3db71fae298e"}