{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FFJMHM7R7QW6BK5YPYC2IQZCTN","short_pith_number":"pith:FFJMHM7R","canonical_record":{"source":{"id":"1812.09688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T11:02:50Z","cross_cats_sorted":[],"title_canon_sha256":"7a3d81e7b524d6d575119b4962c9accbeda8db8c5d86087ab3aab7bd0598bce0","abstract_canon_sha256":"26fd21b26ecc9488bc324296de05d604e5cecdc2ef55b9876fbda44d95ad5b2e"},"schema_version":"1.0"},"canonical_sha256":"2952c3b3f1fc2de0abb87e05a443229b502263a2d1840ede69f563c85732740c","source":{"kind":"arxiv","id":"1812.09688","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09688","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09688v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09688","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"FFJMHM7R7QW6","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FFJMHM7R7QW6BK5Y","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FFJMHM7R","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FFJMHM7R7QW6BK5YPYC2IQZCTN","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T11:02:50Z","cross_cats_sorted":[],"title_canon_sha256":"7a3d81e7b524d6d575119b4962c9accbeda8db8c5d86087ab3aab7bd0598bce0","abstract_canon_sha256":"26fd21b26ecc9488bc324296de05d604e5cecdc2ef55b9876fbda44d95ad5b2e"},"schema_version":"1.0"},"canonical_sha256":"2952c3b3f1fc2de0abb87e05a443229b502263a2d1840ede69f563c85732740c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:27.092679Z","signature_b64":"A66kEtTNNo+p8S84Sc9YRgL46zEVd4z+UdoUs6h++6g8UMWZYXCbBRlhhrD8WkLxivRnPlCSZSSZ6GuvARGKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2952c3b3f1fc2de0abb87e05a443229b502263a2d1840ede69f563c85732740c","last_reissued_at":"2026-05-17T23:57:27.092119Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:27.092119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09688","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":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NH7qJJK08L60H/8pUFQWnQOV1dywWHMtu6xFWQdvWbjp4oTA5p53eLriS65v5T2t9ea0qxDsZHFP5sXXvVMsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:22:07.733109Z"},"content_sha256":"3f371a46199d19e21d26038dcf026b7ec1f583eb13b9dd01cf12b59cf6126a34","schema_version":"1.0","event_id":"sha256:3f371a46199d19e21d26038dcf026b7ec1f583eb13b9dd01cf12b59cf6126a34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FFJMHM7R7QW6BK5YPYC2IQZCTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The depth of a Riemann surface and of a right-angled Artin group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Steve Halperin, Yves Felix","submitted_at":"2018-12-23T11:02:50Z","abstract_excerpt":"We consider two families of spaces, $X$ : the closed orientable Riemann surfaces of genus $g>0$ and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, $L$, that can be determined by the minimal Sullivan algebra. For these spaces we prove that $$ \\mbox{depth} \\,\\mathbb Q[\\pi_1(X)] = \\mbox{depth}\\, {L}\\,$$ and give precise formulas for the depth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09688","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":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOuBVAlbKI27Vw+dx5u2PsEMQI+t4pOC/nH6783saDAkXhCS6luBdUvI+eM1WAGCtkV5XGeXfjtvkj68Of4sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:22:07.733475Z"},"content_sha256":"986b33f656552b47bb11c98d4d0fb02d30181520cdaa87f9b7ef7db7111e6cde","schema_version":"1.0","event_id":"sha256:986b33f656552b47bb11c98d4d0fb02d30181520cdaa87f9b7ef7db7111e6cde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN/bundle.json","state_url":"https://pith.science/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN/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":"2026-06-04T14:22:07Z","links":{"resolver":"https://pith.science/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN","bundle":"https://pith.science/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN/bundle.json","state":"https://pith.science/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFJMHM7R7QW6BK5YPYC2IQZCTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FFJMHM7R7QW6BK5YPYC2IQZCTN","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":"26fd21b26ecc9488bc324296de05d604e5cecdc2ef55b9876fbda44d95ad5b2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T11:02:50Z","title_canon_sha256":"7a3d81e7b524d6d575119b4962c9accbeda8db8c5d86087ab3aab7bd0598bce0"},"schema_version":"1.0","source":{"id":"1812.09688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09688","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09688v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09688","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"FFJMHM7R7QW6","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FFJMHM7R7QW6BK5Y","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FFJMHM7R","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:986b33f656552b47bb11c98d4d0fb02d30181520cdaa87f9b7ef7db7111e6cde","target":"graph","created_at":"2026-05-17T23:57:27Z","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 consider two families of spaces, $X$ : the closed orientable Riemann surfaces of genus $g>0$ and the classifying spaces of right-angled Artin groups. In both cases we compare the depth of the fundamental group with the depth of an associated Lie algebra, $L$, that can be determined by the minimal Sullivan algebra. For these spaces we prove that $$ \\mbox{depth} \\,\\mathbb Q[\\pi_1(X)] = \\mbox{depth}\\, {L}\\,$$ and give precise formulas for the depth.","authors_text":"Steve Halperin, Yves Felix","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T11:02:50Z","title":"The depth of a Riemann surface and of a right-angled Artin group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09688","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":"sha256:3f371a46199d19e21d26038dcf026b7ec1f583eb13b9dd01cf12b59cf6126a34","target":"record","created_at":"2026-05-17T23:57:27Z","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":"26fd21b26ecc9488bc324296de05d604e5cecdc2ef55b9876fbda44d95ad5b2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T11:02:50Z","title_canon_sha256":"7a3d81e7b524d6d575119b4962c9accbeda8db8c5d86087ab3aab7bd0598bce0"},"schema_version":"1.0","source":{"id":"1812.09688","kind":"arxiv","version":1}},"canonical_sha256":"2952c3b3f1fc2de0abb87e05a443229b502263a2d1840ede69f563c85732740c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2952c3b3f1fc2de0abb87e05a443229b502263a2d1840ede69f563c85732740c","first_computed_at":"2026-05-17T23:57:27.092119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:27.092119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A66kEtTNNo+p8S84Sc9YRgL46zEVd4z+UdoUs6h++6g8UMWZYXCbBRlhhrD8WkLxivRnPlCSZSSZ6GuvARGKBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:27.092679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f371a46199d19e21d26038dcf026b7ec1f583eb13b9dd01cf12b59cf6126a34","sha256:986b33f656552b47bb11c98d4d0fb02d30181520cdaa87f9b7ef7db7111e6cde"],"state_sha256":"77b64d7828f5e9b146c866ba0f2af15fbbac41eb5f63663bc0a9516a606fd6de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oEFNhJyaQZuDAYjymb6WWdJaInYhFeCnvbZaqbdFatHUzxKWtypCwsHAAoSVM48R0JVUxnV4pTxhdzi5EWdEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:22:07.735582Z","bundle_sha256":"229e1dbe134523f4a721f08417b091d564e05569941058801c34f2c3509c7ee6"}}