{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TIDU5GVGWGOCO3ZD4Y4BG7ACP6","short_pith_number":"pith:TIDU5GVG","canonical_record":{"source":{"id":"1603.00103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-01T00:19:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1989fb6a43046117dcac96679f42cd4dc6463e2f856d7e0e1939d9d5fb6cd050","abstract_canon_sha256":"9ec4e77c3e25854e0f19c13788e883feff3a19df59dad2da1859a08aafb393b8"},"schema_version":"1.0"},"canonical_sha256":"9a074e9aa6b19c276f23e638137c027f8854d92cffc4875ff6ecd338ca4da6c8","source":{"kind":"arxiv","id":"1603.00103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00103","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00103v1","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00103","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"TIDU5GVGWGOC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIDU5GVGWGOCO3ZD","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIDU5GVG","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TIDU5GVGWGOCO3ZD4Y4BG7ACP6","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-01T00:19:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1989fb6a43046117dcac96679f42cd4dc6463e2f856d7e0e1939d9d5fb6cd050","abstract_canon_sha256":"9ec4e77c3e25854e0f19c13788e883feff3a19df59dad2da1859a08aafb393b8"},"schema_version":"1.0"},"canonical_sha256":"9a074e9aa6b19c276f23e638137c027f8854d92cffc4875ff6ecd338ca4da6c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:49.202618Z","signature_b64":"VdfMYX4xddMrk1ii6KQElVgVuURywwWjISw8Bz7N8p9+wFlQS1MysN0RhBxbTk8IeIDQ7uGQmL19o9BkG+6YCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a074e9aa6b19c276f23e638137c027f8854d92cffc4875ff6ecd338ca4da6c8","last_reissued_at":"2026-05-18T01:19:49.202048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:49.202048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00103","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":"2026-05-18T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAEkmbmNSFJPgSi8d/E8M6Lk50N/+HwM0tgFOLox6a3t0IX0nY90rLLpMzbP2y/F1+AW9hWg/CZUdxy1L0pPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:08:44.172533Z"},"content_sha256":"2b802eaa84f1f19ea8bec81dcc525c476c1f5d949d7cb35be3ec9ff1194f894e","schema_version":"1.0","event_id":"sha256:2b802eaa84f1f19ea8bec81dcc525c476c1f5d949d7cb35be3ec9ff1194f894e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TIDU5GVGWGOCO3ZD4Y4BG7ACP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Assignments for Bott-Samelson manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Catalin Zara, Gouri Shankar Seal","submitted_at":"2016-03-01T00:19:20Z","abstract_excerpt":"Polynomial assignments for a torus $T$-action on a smooth manifold $M$ were introduced by Ginzburg, Guillemin, and Karshon in 1999; they form a module over $\\mathbb{S}(\\mathfrak{t}^*)$, the algebra of polynomial functions on $\\mathfrak{t}$, the Lie algebra of $T$. In this paper we describe the assignment module $\\mathcal{A}_T(M)$ for a natural $T$-action on a Bott-Samelson manifold $M = BS^I$ and present a method for computing generators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00103","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":"2026-05-18T01:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDHmEDf4HpKUcOeYiqmfM8Wok1s0OX+9JLsRXr/jJF+FgpDy+xG/r7rn5zTRLilLlT94eerpi1rjoxQeZFmfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:08:44.173203Z"},"content_sha256":"3ac1db2d90762ea68822b3b1617810dc5ef731f3201d6810160a4f1eb4ee805a","schema_version":"1.0","event_id":"sha256:3ac1db2d90762ea68822b3b1617810dc5ef731f3201d6810160a4f1eb4ee805a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6/bundle.json","state_url":"https://pith.science/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6/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":"2026-06-07T23:08:44Z","links":{"resolver":"https://pith.science/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6","bundle":"https://pith.science/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6/bundle.json","state":"https://pith.science/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIDU5GVGWGOCO3ZD4Y4BG7ACP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TIDU5GVGWGOCO3ZD4Y4BG7ACP6","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":"9ec4e77c3e25854e0f19c13788e883feff3a19df59dad2da1859a08aafb393b8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-01T00:19:20Z","title_canon_sha256":"1989fb6a43046117dcac96679f42cd4dc6463e2f856d7e0e1939d9d5fb6cd050"},"schema_version":"1.0","source":{"id":"1603.00103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00103","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00103v1","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00103","created_at":"2026-05-18T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"TIDU5GVGWGOC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIDU5GVGWGOCO3ZD","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIDU5GVG","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:3ac1db2d90762ea68822b3b1617810dc5ef731f3201d6810160a4f1eb4ee805a","target":"graph","created_at":"2026-05-18T01:19:49Z","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":"Polynomial assignments for a torus $T$-action on a smooth manifold $M$ were introduced by Ginzburg, Guillemin, and Karshon in 1999; they form a module over $\\mathbb{S}(\\mathfrak{t}^*)$, the algebra of polynomial functions on $\\mathfrak{t}$, the Lie algebra of $T$. In this paper we describe the assignment module $\\mathcal{A}_T(M)$ for a natural $T$-action on a Bott-Samelson manifold $M = BS^I$ and present a method for computing generators.","authors_text":"Catalin Zara, Gouri Shankar Seal","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-01T00:19:20Z","title":"Polynomial Assignments for Bott-Samelson manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00103","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":"sha256:2b802eaa84f1f19ea8bec81dcc525c476c1f5d949d7cb35be3ec9ff1194f894e","target":"record","created_at":"2026-05-18T01:19:49Z","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":"9ec4e77c3e25854e0f19c13788e883feff3a19df59dad2da1859a08aafb393b8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-01T00:19:20Z","title_canon_sha256":"1989fb6a43046117dcac96679f42cd4dc6463e2f856d7e0e1939d9d5fb6cd050"},"schema_version":"1.0","source":{"id":"1603.00103","kind":"arxiv","version":1}},"canonical_sha256":"9a074e9aa6b19c276f23e638137c027f8854d92cffc4875ff6ecd338ca4da6c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a074e9aa6b19c276f23e638137c027f8854d92cffc4875ff6ecd338ca4da6c8","first_computed_at":"2026-05-18T01:19:49.202048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:49.202048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VdfMYX4xddMrk1ii6KQElVgVuURywwWjISw8Bz7N8p9+wFlQS1MysN0RhBxbTk8IeIDQ7uGQmL19o9BkG+6YCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:49.202618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b802eaa84f1f19ea8bec81dcc525c476c1f5d949d7cb35be3ec9ff1194f894e","sha256:3ac1db2d90762ea68822b3b1617810dc5ef731f3201d6810160a4f1eb4ee805a"],"state_sha256":"fda0e8ae19bb8090d8a97e6075bf26775fb3cbd44563a503c1bdf47edc9485c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zch+yoeeU9Q0t8DUTuKiMZ2zpi8p1JrPbPwqJQ30doB9VHDOmFFFh/5NVVxddbvG2Ygf5syZYNol2s3w74AgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:08:44.177094Z","bundle_sha256":"b9582ff22444639bdc914397a665714de8d50f5f8fbba71e6111ceab6087ceb5"}}