{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LEQRSJGJUGXYGMVG6N5YKKDGLY","short_pith_number":"pith:LEQRSJGJ","canonical_record":{"source":{"id":"1305.4447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-20T06:36:08Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"a0d7f653319c4965bfd671f4cafcffd1d5cc7010070d03bdf82aff165decfe1a","abstract_canon_sha256":"60733b8cea1b79bc307c946625654cae59ba071fc1ebfed45555f5a7d72f5017"},"schema_version":"1.0"},"canonical_sha256":"59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d","source":{"kind":"arxiv","id":"1305.4447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4447","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4447v1","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4447","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"LEQRSJGJUGXY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LEQRSJGJUGXYGMVG","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LEQRSJGJ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LEQRSJGJUGXYGMVG6N5YKKDGLY","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-20T06:36:08Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"a0d7f653319c4965bfd671f4cafcffd1d5cc7010070d03bdf82aff165decfe1a","abstract_canon_sha256":"60733b8cea1b79bc307c946625654cae59ba071fc1ebfed45555f5a7d72f5017"},"schema_version":"1.0"},"canonical_sha256":"59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:23.669392Z","signature_b64":"uOpGDIPTyp1S6Px6EuZgSxBmjXdCsskembd9KibGHiKRxY4YctdBR/oWFCtI/QSwOBJKbfR9hnICnkp2b/t9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d","last_reissued_at":"2026-05-18T03:25:23.668136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:23.668136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4447","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":"2026-05-18T03:25:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fy3H3n8Cd539Yl77qio8A6YmvSFZCiNWrRDA7KeAPnBAB97TIMT7kaKVleaZ9LNYj0J9/LB81lKwnAZr0J5VDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:08:30.581677Z"},"content_sha256":"7804f3a0a5e6b8f6d778e419bf9b3db483bd403e9511578c7e8111184c533013","schema_version":"1.0","event_id":"sha256:7804f3a0a5e6b8f6d778e419bf9b3db483bd403e9511578c7e8111184c533013"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LEQRSJGJUGXYGMVG6N5YKKDGLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.CO","authors_text":"Christophe Tollu (LIPN), G\\'erard Henry Edmond Duchamp (LIPN), Ladji Kane (LIPN), Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2013-05-20T06:36:08Z","abstract_excerpt":"In this work, an effective construction, via Sch\\\"utzenberger's monoidal factorization, of dual bases for the non commutative symmetric and quasi-symmetric functions is proposed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4447","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":"2026-05-18T03:25:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFuPl3uVNrpMs02QpSme+FAllkRKuErRbRE7RBPHjP0NsPCdeyJUs8WLqMmqvknpR8aRoIEI8PH3BM6bVhRkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:08:30.582028Z"},"content_sha256":"b008aaace14a9130d013422208ec80a52dd39164c061c72e2d6732cfb709b490","schema_version":"1.0","event_id":"sha256:b008aaace14a9130d013422208ec80a52dd39164c061c72e2d6732cfb709b490"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY/bundle.json","state_url":"https://pith.science/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY/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":"2026-06-01T20:08:30Z","links":{"resolver":"https://pith.science/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY","bundle":"https://pith.science/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY/bundle.json","state":"https://pith.science/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEQRSJGJUGXYGMVG6N5YKKDGLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LEQRSJGJUGXYGMVG6N5YKKDGLY","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":"60733b8cea1b79bc307c946625654cae59ba071fc1ebfed45555f5a7d72f5017","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-20T06:36:08Z","title_canon_sha256":"a0d7f653319c4965bfd671f4cafcffd1d5cc7010070d03bdf82aff165decfe1a"},"schema_version":"1.0","source":{"id":"1305.4447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4447","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4447v1","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4447","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"LEQRSJGJUGXY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LEQRSJGJUGXYGMVG","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LEQRSJGJ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:b008aaace14a9130d013422208ec80a52dd39164c061c72e2d6732cfb709b490","target":"graph","created_at":"2026-05-18T03:25:23Z","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":"In this work, an effective construction, via Sch\\\"utzenberger's monoidal factorization, of dual bases for the non commutative symmetric and quasi-symmetric functions is proposed.","authors_text":"Christophe Tollu (LIPN), G\\'erard Henry Edmond Duchamp (LIPN), Ladji Kane (LIPN), Vincel Hoang Ngoc Minh (LIPN)","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-20T06:36:08Z","title":"Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4447","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":"sha256:7804f3a0a5e6b8f6d778e419bf9b3db483bd403e9511578c7e8111184c533013","target":"record","created_at":"2026-05-18T03:25:23Z","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":"60733b8cea1b79bc307c946625654cae59ba071fc1ebfed45555f5a7d72f5017","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-20T06:36:08Z","title_canon_sha256":"a0d7f653319c4965bfd671f4cafcffd1d5cc7010070d03bdf82aff165decfe1a"},"schema_version":"1.0","source":{"id":"1305.4447","kind":"arxiv","version":1}},"canonical_sha256":"59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d","first_computed_at":"2026-05-18T03:25:23.668136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:23.668136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uOpGDIPTyp1S6Px6EuZgSxBmjXdCsskembd9KibGHiKRxY4YctdBR/oWFCtI/QSwOBJKbfR9hnICnkp2b/t9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:23.669392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7804f3a0a5e6b8f6d778e419bf9b3db483bd403e9511578c7e8111184c533013","sha256:b008aaace14a9130d013422208ec80a52dd39164c061c72e2d6732cfb709b490"],"state_sha256":"a2d465ad4f0f8fe1d047b32fa3c54c2f8a0fa9099ef110ffd793f676e4b95d1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QR4AWxeZ9lxqc+CEzvRogR4rPeTtNWQ1t3Du0GQfn34puHHPixwMuWgLbwMlnxyrBxeOPnWOAYdEYGILEN+PBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:08:30.583989Z","bundle_sha256":"ce081a618abe27e0a2bc13f7e7fef4f1653d2790b9a730375fbc3d8b089e0e98"}}