{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7UY5FDZ3BPNIFGG2W6IQHLIH3D","short_pith_number":"pith:7UY5FDZ3","canonical_record":{"source":{"id":"1103.2344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-11T19:07:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"465548878f47f7127afb3fa402c9664ca60e8a7b51794cc39967223448c7d614","abstract_canon_sha256":"465fd686209491d50c5e6a096155cd83da7ed1a4e10cb002fbc6a90f5b12c649"},"schema_version":"1.0"},"canonical_sha256":"fd31d28f3b0bda8298dab79103ad07d8f3d648a2217d7a9111a2a1b388568106","source":{"kind":"arxiv","id":"1103.2344","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2344","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2344v1","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2344","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"pith_short_12","alias_value":"7UY5FDZ3BPNI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7UY5FDZ3BPNIFGG2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7UY5FDZ3","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7UY5FDZ3BPNIFGG2W6IQHLIH3D","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-11T19:07:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"465548878f47f7127afb3fa402c9664ca60e8a7b51794cc39967223448c7d614","abstract_canon_sha256":"465fd686209491d50c5e6a096155cd83da7ed1a4e10cb002fbc6a90f5b12c649"},"schema_version":"1.0"},"canonical_sha256":"fd31d28f3b0bda8298dab79103ad07d8f3d648a2217d7a9111a2a1b388568106","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:01.570681Z","signature_b64":"OUZxZgVPXYutcdUbRcZ358rvlj79jxqQ3XtSFtT3yrazjWM6dMt4ZQvJ/cSWy5Id+9N68o9gpoZ+ShpeFPCZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd31d28f3b0bda8298dab79103ad07d8f3d648a2217d7a9111a2a1b388568106","last_reissued_at":"2026-05-18T03:59:01.569843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:01.569843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2344","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":"2026-05-18T03:59:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcn+iQFDDXK++nyeB4hQKSEXUrfL4F2TYQNvUwFNtwwjWOtmHJqBO0AtgrHCjsbEpaApz3TVqtNMaRSTqK3YBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:28:47.930648Z"},"content_sha256":"ea030ab5409f530ff422d62ed4a61075c5ca9af9c7d96a1c769c5e8c568cc0ac","schema_version":"1.0","event_id":"sha256:ea030ab5409f530ff422d62ed4a61075c5ca9af9c7d96a1c769c5e8c568cc0ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7UY5FDZ3BPNIFGG2W6IQHLIH3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Further results on monoids acting on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"John Rhodes, Pedro V. Silva","submitted_at":"2011-03-11T19:07:16Z","abstract_excerpt":"This paper further develops the theory of arbitrary semigroups acting on trees via elliptic mappings. A key tool is the Lyndon-Chiswell length function L for the semigroup S which allows one to construct a tree T and an action of S on T via elliptic maps. Improving on previous results, the length function of the action will also be L."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2344","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":"2026-05-18T03:59:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgGD3U1Cmd4rZltAV9mwHHmj86n7CsE0xMhogkNfL9i5qdqpZ/eE6UZDKrnEuROo7Zf868NQThX6m0ooSMGxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:28:47.931048Z"},"content_sha256":"18a52aae4caa2e4be111bb4ec2205d584ccb332401d188369f17fb4c96f20d80","schema_version":"1.0","event_id":"sha256:18a52aae4caa2e4be111bb4ec2205d584ccb332401d188369f17fb4c96f20d80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D/bundle.json","state_url":"https://pith.science/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D/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":"2026-05-26T20:28:47Z","links":{"resolver":"https://pith.science/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D","bundle":"https://pith.science/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D/bundle.json","state":"https://pith.science/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UY5FDZ3BPNIFGG2W6IQHLIH3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7UY5FDZ3BPNIFGG2W6IQHLIH3D","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":"465fd686209491d50c5e6a096155cd83da7ed1a4e10cb002fbc6a90f5b12c649","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-11T19:07:16Z","title_canon_sha256":"465548878f47f7127afb3fa402c9664ca60e8a7b51794cc39967223448c7d614"},"schema_version":"1.0","source":{"id":"1103.2344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2344","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2344v1","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2344","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"pith_short_12","alias_value":"7UY5FDZ3BPNI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7UY5FDZ3BPNIFGG2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7UY5FDZ3","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:18a52aae4caa2e4be111bb4ec2205d584ccb332401d188369f17fb4c96f20d80","target":"graph","created_at":"2026-05-18T03:59:01Z","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":"This paper further develops the theory of arbitrary semigroups acting on trees via elliptic mappings. A key tool is the Lyndon-Chiswell length function L for the semigroup S which allows one to construct a tree T and an action of S on T via elliptic maps. Improving on previous results, the length function of the action will also be L.","authors_text":"John Rhodes, Pedro V. Silva","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-11T19:07:16Z","title":"Further results on monoids acting on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2344","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:ea030ab5409f530ff422d62ed4a61075c5ca9af9c7d96a1c769c5e8c568cc0ac","target":"record","created_at":"2026-05-18T03:59:01Z","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":"465fd686209491d50c5e6a096155cd83da7ed1a4e10cb002fbc6a90f5b12c649","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-03-11T19:07:16Z","title_canon_sha256":"465548878f47f7127afb3fa402c9664ca60e8a7b51794cc39967223448c7d614"},"schema_version":"1.0","source":{"id":"1103.2344","kind":"arxiv","version":1}},"canonical_sha256":"fd31d28f3b0bda8298dab79103ad07d8f3d648a2217d7a9111a2a1b388568106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd31d28f3b0bda8298dab79103ad07d8f3d648a2217d7a9111a2a1b388568106","first_computed_at":"2026-05-18T03:59:01.569843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:01.569843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OUZxZgVPXYutcdUbRcZ358rvlj79jxqQ3XtSFtT3yrazjWM6dMt4ZQvJ/cSWy5Id+9N68o9gpoZ+ShpeFPCZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:01.570681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea030ab5409f530ff422d62ed4a61075c5ca9af9c7d96a1c769c5e8c568cc0ac","sha256:18a52aae4caa2e4be111bb4ec2205d584ccb332401d188369f17fb4c96f20d80"],"state_sha256":"0ff25a3bb67d9a840384cbfaee4182207e511858788595d8679a59347d5f2204"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALm0XATmjuNXZq+jkKXzcPi80K98Rxjvi43chPmjY+kZRO9bKEVp5auabl+A8RTsraDcpbVmeLFTkkaHkRBVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:28:47.934077Z","bundle_sha256":"77b409ce749d6bcdbb51bbc7b56cf5f2ff0ead0a2dd2186db7b737c2a84d3173"}}