{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:52X6ZBSJDURIPOE5RGCVZ4J5VL","short_pith_number":"pith:52X6ZBSJ","canonical_record":{"source":{"id":"2509.16296","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2025-09-19T16:12:53Z","cross_cats_sorted":["cs.GT","cs.SY"],"title_canon_sha256":"6ea8a8869f8924b1ca9f2147e2d81c9c5d9a20232f3aabe3100f933fb7d69806","abstract_canon_sha256":"e74379ae9b55076f95def287db22dbc1e169be2494ce097c6636703b3d540d7a"},"schema_version":"1.0"},"canonical_sha256":"eeafec86491d2287b89d89855cf13daaf167a49717bcba635872dcc6d3c4f366","source":{"kind":"arxiv","id":"2509.16296","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.16296","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2509.16296v2","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.16296","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"52X6ZBSJDURI","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"52X6ZBSJDURIPOE5","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"52X6ZBSJ","created_at":"2026-06-02T02:04:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:52X6ZBSJDURIPOE5RGCVZ4J5VL","target":"record","payload":{"canonical_record":{"source":{"id":"2509.16296","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2025-09-19T16:12:53Z","cross_cats_sorted":["cs.GT","cs.SY"],"title_canon_sha256":"6ea8a8869f8924b1ca9f2147e2d81c9c5d9a20232f3aabe3100f933fb7d69806","abstract_canon_sha256":"e74379ae9b55076f95def287db22dbc1e169be2494ce097c6636703b3d540d7a"},"schema_version":"1.0"},"canonical_sha256":"eeafec86491d2287b89d89855cf13daaf167a49717bcba635872dcc6d3c4f366","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:08.834238Z","signature_b64":"U2tiJ2aUVbVPrz02ovtX3RclQJNQf/IBkKPac2cOzCUDV+pv5N3vEwazMMYc8XkzxpwAgAKVVqgwD161FJc7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeafec86491d2287b89d89855cf13daaf167a49717bcba635872dcc6d3c4f366","last_reissued_at":"2026-06-02T02:04:08.833660Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:08.833660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.16296","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":"2026-06-02T02:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yq3SRqtB1+U2Jn76em26mNhDbwsxyMxvIUMX9sLvYd227Y+94mIaC/wmpEEwVjACI+NnWjKWdd/5UPA+XUNdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:42:27.534592Z"},"content_sha256":"cb9e1dc6777231b006f8affadaeb88d62e9b26794640d62c08c0851b179cf1c3","schema_version":"1.0","event_id":"sha256:cb9e1dc6777231b006f8affadaeb88d62e9b26794640d62c08c0851b179cf1c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:52X6ZBSJDURIPOE5RGCVZ4J5VL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning in Stackelberg Markov Games","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.GT","cs.SY"],"primary_cat":"eess.SY","authors_text":"Andrew L. Liu, Jun He, Yihsu Chen","submitted_at":"2025-09-19T16:12:53Z","abstract_excerpt":"Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain environments, where a single leader interacts with a population of adaptive followers. Motivated by pressing real-world challenges such as equitable electricity tariff design for consumers with distributed energy resources (such as rooftop solar and energy storage), we formalize a class of Stackelberg Markov games and establish the existence and uniqueness of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.16296","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/2509.16296/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":"2026-06-02T02:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBBJ+9rDEO13wGHqPoDTtKE/+6w4+Lbyi81TlItyX6DFVMTEoXcJLkgQVmd0bxFxlIAas7W2Z7KKnIC5bPy0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:42:27.534994Z"},"content_sha256":"f0dff01eeff6373f0026b2b4b9bb119fbaaa540667e4e0694c04dac9ad7c8230","schema_version":"1.0","event_id":"sha256:f0dff01eeff6373f0026b2b4b9bb119fbaaa540667e4e0694c04dac9ad7c8230"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL/bundle.json","state_url":"https://pith.science/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL/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":"2026-06-02T21:42:27Z","links":{"resolver":"https://pith.science/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL","bundle":"https://pith.science/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL/bundle.json","state":"https://pith.science/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52X6ZBSJDURIPOE5RGCVZ4J5VL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:52X6ZBSJDURIPOE5RGCVZ4J5VL","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":"e74379ae9b55076f95def287db22dbc1e169be2494ce097c6636703b3d540d7a","cross_cats_sorted":["cs.GT","cs.SY"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2025-09-19T16:12:53Z","title_canon_sha256":"6ea8a8869f8924b1ca9f2147e2d81c9c5d9a20232f3aabe3100f933fb7d69806"},"schema_version":"1.0","source":{"id":"2509.16296","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.16296","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2509.16296v2","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.16296","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"52X6ZBSJDURI","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"52X6ZBSJDURIPOE5","created_at":"2026-06-02T02:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"52X6ZBSJ","created_at":"2026-06-02T02:04:08Z"}],"graph_snapshots":[{"event_id":"sha256:f0dff01eeff6373f0026b2b4b9bb119fbaaa540667e4e0694c04dac9ad7c8230","target":"graph","created_at":"2026-06-02T02:04:08Z","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/2509.16296/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain environments, where a single leader interacts with a population of adaptive followers. Motivated by pressing real-world challenges such as equitable electricity tariff design for consumers with distributed energy resources (such as rooftop solar and energy storage), we formalize a class of Stackelberg Markov games and establish the existence and uniqueness of ","authors_text":"Andrew L. Liu, Jun He, Yihsu Chen","cross_cats":["cs.GT","cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2025-09-19T16:12:53Z","title":"Learning in Stackelberg Markov Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.16296","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:cb9e1dc6777231b006f8affadaeb88d62e9b26794640d62c08c0851b179cf1c3","target":"record","created_at":"2026-06-02T02:04:08Z","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":"e74379ae9b55076f95def287db22dbc1e169be2494ce097c6636703b3d540d7a","cross_cats_sorted":["cs.GT","cs.SY"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2025-09-19T16:12:53Z","title_canon_sha256":"6ea8a8869f8924b1ca9f2147e2d81c9c5d9a20232f3aabe3100f933fb7d69806"},"schema_version":"1.0","source":{"id":"2509.16296","kind":"arxiv","version":2}},"canonical_sha256":"eeafec86491d2287b89d89855cf13daaf167a49717bcba635872dcc6d3c4f366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeafec86491d2287b89d89855cf13daaf167a49717bcba635872dcc6d3c4f366","first_computed_at":"2026-06-02T02:04:08.833660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:08.833660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U2tiJ2aUVbVPrz02ovtX3RclQJNQf/IBkKPac2cOzCUDV+pv5N3vEwazMMYc8XkzxpwAgAKVVqgwD161FJc7Cg==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:08.834238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.16296","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb9e1dc6777231b006f8affadaeb88d62e9b26794640d62c08c0851b179cf1c3","sha256:f0dff01eeff6373f0026b2b4b9bb119fbaaa540667e4e0694c04dac9ad7c8230"],"state_sha256":"a8f5cb9e530f15c17c00beeafcbbe128ea49f492c9c327931364fa8804b28455"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ip3NcPGNckbeX+3WSWDR3GXyA37xKI+i+JSn5sp1qulyfT3VfRpuFoUZHKqubuDjdGRH9aRCi//GIK5OI5zBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:42:27.537033Z","bundle_sha256":"59bafe65e0585e7ce884739396d54eb3bc4c1088b922c3ba2a4aff40cfd6e700"}}