{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NUDQ5U5L6AWLKTDBALCMUYUM5A","short_pith_number":"pith:NUDQ5U5L","canonical_record":{"source":{"id":"2605.24327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-23T01:16:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"300db62f6f00b26c7b014ef558857d66f839a345ebea3371abd93d24e6cfc1c1","abstract_canon_sha256":"7ef01f7a2591f54a0f6c272ab74f630ab1cfb836f620c4b8a33e7816f32bf24c"},"schema_version":"1.0"},"canonical_sha256":"6d070ed3abf02cb54c6102c4ca628ce8066104c2aa2647d1bfeb76d0c5daffe2","source":{"kind":"arxiv","id":"2605.24327","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24327","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24327v1","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24327","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"NUDQ5U5L6AWL","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"pith_short_16","alias_value":"NUDQ5U5L6AWLKTDB","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"pith_short_8","alias_value":"NUDQ5U5L","created_at":"2026-05-26T01:03:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NUDQ5U5L6AWLKTDBALCMUYUM5A","target":"record","payload":{"canonical_record":{"source":{"id":"2605.24327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-23T01:16:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"300db62f6f00b26c7b014ef558857d66f839a345ebea3371abd93d24e6cfc1c1","abstract_canon_sha256":"7ef01f7a2591f54a0f6c272ab74f630ab1cfb836f620c4b8a33e7816f32bf24c"},"schema_version":"1.0"},"canonical_sha256":"6d070ed3abf02cb54c6102c4ca628ce8066104c2aa2647d1bfeb76d0c5daffe2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:00.186053Z","signature_b64":"BIm2kaZ6qfSfgGqREipihTE1MprBWtiCklxvVrdUqW6+uCF4GxzLTzdhB2iOK3DvU3cKfnmK9UigbnCMWIl+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d070ed3abf02cb54c6102c4ca628ce8066104c2aa2647d1bfeb76d0c5daffe2","last_reissued_at":"2026-05-26T01:03:00.185273Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:00.185273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.24327","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":"2026-05-26T01:03:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e1Hhch/Vgq2gMT6IeE3g2R+MCTiNbfGcCwmob2r6JZlktX+FJHgcgmoa1kb8yVl0Nht8fZ+0CCgxRtqHG61/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:11:16.747883Z"},"content_sha256":"4f322bb0fe1d65e6c44cd139840c6cee0620cd0eb393b38e7982ed991acdb568","schema_version":"1.0","event_id":"sha256:4f322bb0fe1d65e6c44cd139840c6cee0620cd0eb393b38e7982ed991acdb568"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NUDQ5U5L6AWLKTDBALCMUYUM5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Jonah Berggren","submitted_at":"2026-05-23T01:16:37Z","abstract_excerpt":"In the study of flow polytopes, a directed acyclic graph (DAG) with a choice of framing gives a regular unimodular triangulation on its space of unit nonnegative flows. In representation theory, a gentle algebra has recently been equipped with a space of unit flows admitting triangulation and subdivision results capturing its tau-tilting theory. These theories from different areas of mathematics overlap: flows on gently framed DAGs are the same as flows on paired representation-finite gentle algebras. In this article we develop the common generalization of these two theories by defining (frame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24327","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24327/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":"2026-05-26T01:03:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5kkl6fUdDfcNVVqsg5kqDXDcowFZFcSXmQ8IpnGNk/xv5wUm7K598/g8ziM91FGkfgWRtW+yZiON+xQqD91AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:11:16.748261Z"},"content_sha256":"45ded88701bda03e104cd1d23d8713c3218d503f2bc7b02acb3440374a25d73a","schema_version":"1.0","event_id":"sha256:45ded88701bda03e104cd1d23d8713c3218d503f2bc7b02acb3440374a25d73a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A/bundle.json","state_url":"https://pith.science/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A/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":"2026-06-25T08:11:16Z","links":{"resolver":"https://pith.science/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A","bundle":"https://pith.science/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A/bundle.json","state":"https://pith.science/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUDQ5U5L6AWLKTDBALCMUYUM5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NUDQ5U5L6AWLKTDBALCMUYUM5A","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":"7ef01f7a2591f54a0f6c272ab74f630ab1cfb836f620c4b8a33e7816f32bf24c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-23T01:16:37Z","title_canon_sha256":"300db62f6f00b26c7b014ef558857d66f839a345ebea3371abd93d24e6cfc1c1"},"schema_version":"1.0","source":{"id":"2605.24327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24327","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24327v1","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24327","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"NUDQ5U5L6AWL","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"pith_short_16","alias_value":"NUDQ5U5L6AWLKTDB","created_at":"2026-05-26T01:03:00Z"},{"alias_kind":"pith_short_8","alias_value":"NUDQ5U5L","created_at":"2026-05-26T01:03:00Z"}],"graph_snapshots":[{"event_id":"sha256:45ded88701bda03e104cd1d23d8713c3218d503f2bc7b02acb3440374a25d73a","target":"graph","created_at":"2026-05-26T01:03:00Z","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/2605.24327/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the study of flow polytopes, a directed acyclic graph (DAG) with a choice of framing gives a regular unimodular triangulation on its space of unit nonnegative flows. In representation theory, a gentle algebra has recently been equipped with a space of unit flows admitting triangulation and subdivision results capturing its tau-tilting theory. These theories from different areas of mathematics overlap: flows on gently framed DAGs are the same as flows on paired representation-finite gentle algebras. In this article we develop the common generalization of these two theories by defining (frame","authors_text":"Jonah Berggren","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-23T01:16:37Z","title":"On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24327","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":"sha256:4f322bb0fe1d65e6c44cd139840c6cee0620cd0eb393b38e7982ed991acdb568","target":"record","created_at":"2026-05-26T01:03:00Z","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":"7ef01f7a2591f54a0f6c272ab74f630ab1cfb836f620c4b8a33e7816f32bf24c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-23T01:16:37Z","title_canon_sha256":"300db62f6f00b26c7b014ef558857d66f839a345ebea3371abd93d24e6cfc1c1"},"schema_version":"1.0","source":{"id":"2605.24327","kind":"arxiv","version":1}},"canonical_sha256":"6d070ed3abf02cb54c6102c4ca628ce8066104c2aa2647d1bfeb76d0c5daffe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d070ed3abf02cb54c6102c4ca628ce8066104c2aa2647d1bfeb76d0c5daffe2","first_computed_at":"2026-05-26T01:03:00.185273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:00.185273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BIm2kaZ6qfSfgGqREipihTE1MprBWtiCklxvVrdUqW6+uCF4GxzLTzdhB2iOK3DvU3cKfnmK9UigbnCMWIl+AQ==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:00.186053Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f322bb0fe1d65e6c44cd139840c6cee0620cd0eb393b38e7982ed991acdb568","sha256:45ded88701bda03e104cd1d23d8713c3218d503f2bc7b02acb3440374a25d73a"],"state_sha256":"98cd248cbb2565831e771ef4a9b9998177f9c76f8bac997a02757f1ba0987cc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+EEN7VC/hTa5SwQ8kaMlqS9fBtBoo7WFtWPeIqhgHddHRmAzpMmVHwIgIqohW/6Ii82haB5yOk5xw1D6thKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:11:16.750265Z","bundle_sha256":"273c544055f89b09c25735ac403a61f63b4ad6355cdb46a8d3ed1fb815e191c2"}}