{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:32AV6QB4P32FVJKBOH5MICBWHZ","short_pith_number":"pith:32AV6QB4","canonical_record":{"source":{"id":"2603.23809","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-03-25T00:38:58Z","cross_cats_sorted":["math.CO","math.GR","math.LO"],"title_canon_sha256":"62c081537e879223e9bd50c6467eef20a5c84f0111bf52099fb3b476deaee71d","abstract_canon_sha256":"e8ce16c86e302f65b5723b4002ceb4515a02e7f32c9aeb083eb56c996de94262"},"schema_version":"1.0"},"canonical_sha256":"de815f403c7ef45aa54171fac408363e5f0ba7d405d36e737412db826403a047","source":{"kind":"arxiv","id":"2603.23809","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.23809","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2603.23809v2","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.23809","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"32AV6QB4P32F","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"32AV6QB4P32FVJKB","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"32AV6QB4","created_at":"2026-05-22T01:04:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:32AV6QB4P32FVJKBOH5MICBWHZ","target":"record","payload":{"canonical_record":{"source":{"id":"2603.23809","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-03-25T00:38:58Z","cross_cats_sorted":["math.CO","math.GR","math.LO"],"title_canon_sha256":"62c081537e879223e9bd50c6467eef20a5c84f0111bf52099fb3b476deaee71d","abstract_canon_sha256":"e8ce16c86e302f65b5723b4002ceb4515a02e7f32c9aeb083eb56c996de94262"},"schema_version":"1.0"},"canonical_sha256":"de815f403c7ef45aa54171fac408363e5f0ba7d405d36e737412db826403a047","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:55.256961Z","signature_b64":"UThgipKS6544NmCXLt85nuU7oaB3SwF2ntNbhnFnP0Ox3ScWMTiUhNwloa5hT16g7SnQYct3VY03/k3PqtmcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de815f403c7ef45aa54171fac408363e5f0ba7d405d36e737412db826403a047","last_reissued_at":"2026-05-22T01:04:55.256081Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:55.256081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.23809","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGmNz6SAcG9PVlYdrMtj2xIKzw9caxHvhJkh5YhXkn6TNSzq+b0ka/0wYOH0FOoQSi36UJUjl4fnsSU6n8X3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:45:59.616112Z"},"content_sha256":"34fa8b6c981cb4b6dbb6bc25d6c7b598999f0b07438f07d52b8bc2c0beab42f5","schema_version":"1.0","event_id":"sha256:34fa8b6c981cb4b6dbb6bc25d6c7b598999f0b07438f07d52b8bc2c0beab42f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:32AV6QB4P32FVJKBOH5MICBWHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite sequences via Lie algebra actions for oligomorphic groups","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO","math.GR","math.LO"],"primary_cat":"math.RT","authors_text":"Zbigniew Wojciechowski","submitted_at":"2026-03-25T00:38:58Z","abstract_excerpt":"Many integer sequences arise as numbers of $G$-orbits on $\\binom{X}{n}$ as $n$ varies, for a permutation group $G\\subseteq \\operatorname{Sym}(X)$. For finite $X$, Stanley proved that these finite sequences increase towards the middle using an action of the Lie algebra $\\mathfrak{sl}_2(\\mathbb{C})$. For infinite sets $X$, and hence infinite sequences, Cameron provided an argument for monotonicity by identifying orbits with a vector space basis of the orbit algebra $\\mathsf{H}_{G,X}^{\\star}$, and proving injectivity of a certain operator $\\mathsf{H}_{G,X}^{\\star}\\to \\mathsf{H}_{G,X}^{\\star+1}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.23809","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.23809/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-22T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f+XUDHsUBbP2wLfBGZMdDdJH9JtmnCU9qPl1ZJrT5dzxdP4dUPoeYBQSX2iuLcp61hzr5vr7/muj1AhgNvddCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:45:59.616504Z"},"content_sha256":"d9bc0b06a2fe9240ea47451ed440eab62c4352a4dcb05d2cb678c8c4d41dc9ea","schema_version":"1.0","event_id":"sha256:d9bc0b06a2fe9240ea47451ed440eab62c4352a4dcb05d2cb678c8c4d41dc9ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32AV6QB4P32FVJKBOH5MICBWHZ/bundle.json","state_url":"https://pith.science/pith/32AV6QB4P32FVJKBOH5MICBWHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32AV6QB4P32FVJKBOH5MICBWHZ/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":"2026-06-04T06:45:59Z","links":{"resolver":"https://pith.science/pith/32AV6QB4P32FVJKBOH5MICBWHZ","bundle":"https://pith.science/pith/32AV6QB4P32FVJKBOH5MICBWHZ/bundle.json","state":"https://pith.science/pith/32AV6QB4P32FVJKBOH5MICBWHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32AV6QB4P32FVJKBOH5MICBWHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:32AV6QB4P32FVJKBOH5MICBWHZ","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":"e8ce16c86e302f65b5723b4002ceb4515a02e7f32c9aeb083eb56c996de94262","cross_cats_sorted":["math.CO","math.GR","math.LO"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-03-25T00:38:58Z","title_canon_sha256":"62c081537e879223e9bd50c6467eef20a5c84f0111bf52099fb3b476deaee71d"},"schema_version":"1.0","source":{"id":"2603.23809","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.23809","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2603.23809v2","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.23809","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"32AV6QB4P32F","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"32AV6QB4P32FVJKB","created_at":"2026-05-22T01:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"32AV6QB4","created_at":"2026-05-22T01:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:d9bc0b06a2fe9240ea47451ed440eab62c4352a4dcb05d2cb678c8c4d41dc9ea","target":"graph","created_at":"2026-05-22T01:04:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2603.23809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many integer sequences arise as numbers of $G$-orbits on $\\binom{X}{n}$ as $n$ varies, for a permutation group $G\\subseteq \\operatorname{Sym}(X)$. For finite $X$, Stanley proved that these finite sequences increase towards the middle using an action of the Lie algebra $\\mathfrak{sl}_2(\\mathbb{C})$. For infinite sets $X$, and hence infinite sequences, Cameron provided an argument for monotonicity by identifying orbits with a vector space basis of the orbit algebra $\\mathsf{H}_{G,X}^{\\star}$, and proving injectivity of a certain operator $\\mathsf{H}_{G,X}^{\\star}\\to \\mathsf{H}_{G,X}^{\\star+1}$. ","authors_text":"Zbigniew Wojciechowski","cross_cats":["math.CO","math.GR","math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-03-25T00:38:58Z","title":"Infinite sequences via Lie algebra actions for oligomorphic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.23809","kind":"arxiv","version":2},"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":"sha256:34fa8b6c981cb4b6dbb6bc25d6c7b598999f0b07438f07d52b8bc2c0beab42f5","target":"record","created_at":"2026-05-22T01:04:55Z","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":"e8ce16c86e302f65b5723b4002ceb4515a02e7f32c9aeb083eb56c996de94262","cross_cats_sorted":["math.CO","math.GR","math.LO"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RT","submitted_at":"2026-03-25T00:38:58Z","title_canon_sha256":"62c081537e879223e9bd50c6467eef20a5c84f0111bf52099fb3b476deaee71d"},"schema_version":"1.0","source":{"id":"2603.23809","kind":"arxiv","version":2}},"canonical_sha256":"de815f403c7ef45aa54171fac408363e5f0ba7d405d36e737412db826403a047","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de815f403c7ef45aa54171fac408363e5f0ba7d405d36e737412db826403a047","first_computed_at":"2026-05-22T01:04:55.256081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:55.256081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UThgipKS6544NmCXLt85nuU7oaB3SwF2ntNbhnFnP0Ox3ScWMTiUhNwloa5hT16g7SnQYct3VY03/k3PqtmcDw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:55.256961Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.23809","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34fa8b6c981cb4b6dbb6bc25d6c7b598999f0b07438f07d52b8bc2c0beab42f5","sha256:d9bc0b06a2fe9240ea47451ed440eab62c4352a4dcb05d2cb678c8c4d41dc9ea"],"state_sha256":"870b918230b48b1c11f7cf021e1cff5117a19fac4e19e26e749b0719cc446378"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQaLym2PsjsG7WlaQitlKYxtrTspHn7G0+fdwaCECjace2MCG1zGADjTdoE33ZLJqlM/xOAgzt27d2TZWxVyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:45:59.618436Z","bundle_sha256":"c8a812d090740aaa73d5919755d53bb9bf86f8d25113aa2da2635db8da4a87bc"}}