{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MDOQ6Z756DT7OGSPSPOMWB5VTU","short_pith_number":"pith:MDOQ6Z75","canonical_record":{"source":{"id":"1507.00958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-03T15:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"0f17ba831d07cfa8517b94265171a05236b4a900325fbcbb230ee8fcaab0fa6a","abstract_canon_sha256":"a016aa90c473ed4ebd59d0762225f5ef854d8829b03ffae7d6c85796c567e9fb"},"schema_version":"1.0"},"canonical_sha256":"60dd0f67fdf0e7f71a4f93dccb07b59d1e4c3a4b3238ae5b396c7c8581eec8dd","source":{"kind":"arxiv","id":"1507.00958","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00958","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00958v1","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00958","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"MDOQ6Z756DT7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MDOQ6Z756DT7OGSP","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MDOQ6Z75","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MDOQ6Z756DT7OGSPSPOMWB5VTU","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-03T15:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"0f17ba831d07cfa8517b94265171a05236b4a900325fbcbb230ee8fcaab0fa6a","abstract_canon_sha256":"a016aa90c473ed4ebd59d0762225f5ef854d8829b03ffae7d6c85796c567e9fb"},"schema_version":"1.0"},"canonical_sha256":"60dd0f67fdf0e7f71a4f93dccb07b59d1e4c3a4b3238ae5b396c7c8581eec8dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:22.159397Z","signature_b64":"uMY6GIlSTm+7U0xK/gxwvpvgqOccF+F1JPBFKUnwuctP+5Tn089uYLeRlXeNKTYJyJayZNr5/bir7dH/+ycVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60dd0f67fdf0e7f71a4f93dccb07b59d1e4c3a4b3238ae5b396c7c8581eec8dd","last_reissued_at":"2026-05-18T01:37:22.158730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:22.158730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00958","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":"2026-05-18T01:37:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qtTmLkuAZ3eScBRKUq0I9tIElaQGXqmM30LtknVWqOmYIpF3CX/Iwta+LH9zhejd1YUK+yu8LzQ7G6DoYWiLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:14:59.588088Z"},"content_sha256":"b1243a38719c1e5312e7f653f94cf6ecd940e0454ae034de1bbe65f9eacb0c85","schema_version":"1.0","event_id":"sha256:b1243a38719c1e5312e7f653f94cf6ecd940e0454ae034de1bbe65f9eacb0c85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MDOQ6Z756DT7OGSPSPOMWB5VTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fans and generators of free abelian l-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daniele Mundici","submitted_at":"2015-07-03T15:59:39Z","abstract_excerpt":"Let $t_1,\\ldots,t_n$ be $\\ell$-group terms in the variables $X_1,\\ldots,X_m$. Let $\\hat t_1,\\ldots,\\hat t_n$ be their associated piecewise homogeneous linear functions. Let $G $ be the $\\ell$-group generated by $\\hat t_1, \\ldots,\\hat t_n$ in the free $m$-generator $\\ell$-group $\\mathcal A_m.$ We prove: (i) the problem whether $G$ is $\\ell$-isomorphic to $\\mathcal A_n$ is decidable; (ii) the problem whether $G$ is $\\ell$-isomorphic to $\\mathcal A_l$ ($l$ arbitrary) is undecidable; (iii) for $m=n$, the problem whether $\\{\\hat t_1,\\ldots,\\hat t_n\\}$ is a {\\it free} generating set is decidable. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00958","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":"2026-05-18T01:37:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqL6wMYl0KyyoEF2MX3IDYtMKpDJC7HkaSkk8y1sYat7iKzRUddqo8J1U+BSXuZzcpJUCqo7QMH8oLViuvKqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:14:59.588757Z"},"content_sha256":"7e131c4792f5bf70ccfe1f46904ca221e266d96c1f1d55538a084c8635e0c0cf","schema_version":"1.0","event_id":"sha256:7e131c4792f5bf70ccfe1f46904ca221e266d96c1f1d55538a084c8635e0c0cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU/bundle.json","state_url":"https://pith.science/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU/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":"2026-06-08T00:14:59Z","links":{"resolver":"https://pith.science/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU","bundle":"https://pith.science/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU/bundle.json","state":"https://pith.science/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDOQ6Z756DT7OGSPSPOMWB5VTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MDOQ6Z756DT7OGSPSPOMWB5VTU","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":"a016aa90c473ed4ebd59d0762225f5ef854d8829b03ffae7d6c85796c567e9fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-03T15:59:39Z","title_canon_sha256":"0f17ba831d07cfa8517b94265171a05236b4a900325fbcbb230ee8fcaab0fa6a"},"schema_version":"1.0","source":{"id":"1507.00958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00958","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00958v1","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00958","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"MDOQ6Z756DT7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MDOQ6Z756DT7OGSP","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MDOQ6Z75","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:7e131c4792f5bf70ccfe1f46904ca221e266d96c1f1d55538a084c8635e0c0cf","target":"graph","created_at":"2026-05-18T01:37:22Z","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":"Let $t_1,\\ldots,t_n$ be $\\ell$-group terms in the variables $X_1,\\ldots,X_m$. Let $\\hat t_1,\\ldots,\\hat t_n$ be their associated piecewise homogeneous linear functions. Let $G $ be the $\\ell$-group generated by $\\hat t_1, \\ldots,\\hat t_n$ in the free $m$-generator $\\ell$-group $\\mathcal A_m.$ We prove: (i) the problem whether $G$ is $\\ell$-isomorphic to $\\mathcal A_n$ is decidable; (ii) the problem whether $G$ is $\\ell$-isomorphic to $\\mathcal A_l$ ($l$ arbitrary) is undecidable; (iii) for $m=n$, the problem whether $\\{\\hat t_1,\\ldots,\\hat t_n\\}$ is a {\\it free} generating set is decidable. In","authors_text":"Daniele Mundici","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-03T15:59:39Z","title":"Fans and generators of free abelian l-groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00958","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:b1243a38719c1e5312e7f653f94cf6ecd940e0454ae034de1bbe65f9eacb0c85","target":"record","created_at":"2026-05-18T01:37:22Z","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":"a016aa90c473ed4ebd59d0762225f5ef854d8829b03ffae7d6c85796c567e9fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-07-03T15:59:39Z","title_canon_sha256":"0f17ba831d07cfa8517b94265171a05236b4a900325fbcbb230ee8fcaab0fa6a"},"schema_version":"1.0","source":{"id":"1507.00958","kind":"arxiv","version":1}},"canonical_sha256":"60dd0f67fdf0e7f71a4f93dccb07b59d1e4c3a4b3238ae5b396c7c8581eec8dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60dd0f67fdf0e7f71a4f93dccb07b59d1e4c3a4b3238ae5b396c7c8581eec8dd","first_computed_at":"2026-05-18T01:37:22.158730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:22.158730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uMY6GIlSTm+7U0xK/gxwvpvgqOccF+F1JPBFKUnwuctP+5Tn089uYLeRlXeNKTYJyJayZNr5/bir7dH/+ycVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:22.159397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1243a38719c1e5312e7f653f94cf6ecd940e0454ae034de1bbe65f9eacb0c85","sha256:7e131c4792f5bf70ccfe1f46904ca221e266d96c1f1d55538a084c8635e0c0cf"],"state_sha256":"75de2221227d7f4738b008e880b03a304ae4634b0467a3df5d25a3f1a291b22d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJY/BMTj8kinr0UyGdT5K4uuQAELZjTFK7s0iBPRv46lG22rJBDDbC4E6IqBwBZTTdCC0gut8ilWF8ERxB13BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T00:14:59.592865Z","bundle_sha256":"3aa62fef4d5abb3e0d7f468c48557ef75cc2bc910a78255a5ef0ee7d049a7a6c"}}