{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CNB23C7LDREOUO2OOWYEDN35IW","short_pith_number":"pith:CNB23C7L","canonical_record":{"source":{"id":"2107.03139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-07-07T10:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"1ad841489b202a1305434fefc2708f3ba4ed83fffcdcebabf97a64ec14bbbaac","abstract_canon_sha256":"6fa435f5e17c2bc5033d13831d9f6b3086287e5d049a5d648e0b71d1289b4c6c"},"schema_version":"1.0"},"canonical_sha256":"1343ad8beb1c48ea3b4e75b041b77d45a73d7e5ee639583eb2b1be69ac0584f8","source":{"kind":"arxiv","id":"2107.03139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03139","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03139v1","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03139","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"CNB23C7LDREO","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"pith_short_16","alias_value":"CNB23C7LDREOUO2O","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"pith_short_8","alias_value":"CNB23C7L","created_at":"2026-07-05T02:56:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CNB23C7LDREOUO2OOWYEDN35IW","target":"record","payload":{"canonical_record":{"source":{"id":"2107.03139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-07-07T10:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"1ad841489b202a1305434fefc2708f3ba4ed83fffcdcebabf97a64ec14bbbaac","abstract_canon_sha256":"6fa435f5e17c2bc5033d13831d9f6b3086287e5d049a5d648e0b71d1289b4c6c"},"schema_version":"1.0"},"canonical_sha256":"1343ad8beb1c48ea3b4e75b041b77d45a73d7e5ee639583eb2b1be69ac0584f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:00.967274Z","signature_b64":"sJwptKiBYyEsmkMmj4dE7S/hyb56fL3q+xsKNGmvsWp/MyrP5+KvTqIZFZHVWZ8cpYkPqAe/bY1j7OT8xMT7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1343ad8beb1c48ea3b4e75b041b77d45a73d7e5ee639583eb2b1be69ac0584f8","last_reissued_at":"2026-07-05T02:56:00.966935Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:00.966935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.03139","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":"2026-07-05T02:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ER3YNkwZpMaGhbMHtSSaNAeedhqoTj0gnjg24J8WcIbTnbZHuVFkuk3/Sw1/Z5RPleSa4KGOlZrtwNHdIEbZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:10:24.787301Z"},"content_sha256":"19d633d5e64358ef7ee4261793a873d62a1a4d67bfc674daeecaba957d400655","schema_version":"1.0","event_id":"sha256:19d633d5e64358ef7ee4261793a873d62a1a4d67bfc674daeecaba957d400655"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CNB23C7LDREOUO2OOWYEDN35IW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tropicalization of toric prevarieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex K\\\"uronya, Martin Ulirsch, Pedro Souza","submitted_at":"2021-07-07T10:56:01Z","abstract_excerpt":"The homogeneous spectrum of a multigraded finitely generated algebra (in the sense of Brenner-Schr\\\"oer) always admits an embedding into a toric variety that is not necessarily separated, a so-called toric prevariety. In order to have a convenient framework to study the tropicalization of homogeneous spectra we propose a tropicalization procedure for toric prevarieties and study its basic properties. With these tools at hand, we prove a generalization of Payne's and Foster--Gross--Payne's tropical limit theorem for divisorial schemes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03139","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/2107.03139/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":"2026-07-05T02:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rnd9lt4Oy+9Xt2kFgPGL8Kfq3CpFqRppWNOJrge8eTuk2CzPJIzZ2PJpp8s/4QzIsMUJhQ158YLghC/o127GDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:10:24.787683Z"},"content_sha256":"376d22b626bc4e67eda86ddff163b83dca629e24f58fc43a4398d56b01212ef6","schema_version":"1.0","event_id":"sha256:376d22b626bc4e67eda86ddff163b83dca629e24f58fc43a4398d56b01212ef6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNB23C7LDREOUO2OOWYEDN35IW/bundle.json","state_url":"https://pith.science/pith/CNB23C7LDREOUO2OOWYEDN35IW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNB23C7LDREOUO2OOWYEDN35IW/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":"2026-08-13T17:10:24Z","links":{"resolver":"https://pith.science/pith/CNB23C7LDREOUO2OOWYEDN35IW","bundle":"https://pith.science/pith/CNB23C7LDREOUO2OOWYEDN35IW/bundle.json","state":"https://pith.science/pith/CNB23C7LDREOUO2OOWYEDN35IW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNB23C7LDREOUO2OOWYEDN35IW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CNB23C7LDREOUO2OOWYEDN35IW","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":"6fa435f5e17c2bc5033d13831d9f6b3086287e5d049a5d648e0b71d1289b4c6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-07-07T10:56:01Z","title_canon_sha256":"1ad841489b202a1305434fefc2708f3ba4ed83fffcdcebabf97a64ec14bbbaac"},"schema_version":"1.0","source":{"id":"2107.03139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03139","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03139v1","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03139","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"CNB23C7LDREO","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"pith_short_16","alias_value":"CNB23C7LDREOUO2O","created_at":"2026-07-05T02:56:00Z"},{"alias_kind":"pith_short_8","alias_value":"CNB23C7L","created_at":"2026-07-05T02:56:00Z"}],"graph_snapshots":[{"event_id":"sha256:376d22b626bc4e67eda86ddff163b83dca629e24f58fc43a4398d56b01212ef6","target":"graph","created_at":"2026-07-05T02:56:00Z","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/2107.03139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The homogeneous spectrum of a multigraded finitely generated algebra (in the sense of Brenner-Schr\\\"oer) always admits an embedding into a toric variety that is not necessarily separated, a so-called toric prevariety. In order to have a convenient framework to study the tropicalization of homogeneous spectra we propose a tropicalization procedure for toric prevarieties and study its basic properties. With these tools at hand, we prove a generalization of Payne's and Foster--Gross--Payne's tropical limit theorem for divisorial schemes.","authors_text":"Alex K\\\"uronya, Martin Ulirsch, Pedro Souza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-07-07T10:56:01Z","title":"Tropicalization of toric prevarieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03139","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":"sha256:19d633d5e64358ef7ee4261793a873d62a1a4d67bfc674daeecaba957d400655","target":"record","created_at":"2026-07-05T02:56:00Z","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":"6fa435f5e17c2bc5033d13831d9f6b3086287e5d049a5d648e0b71d1289b4c6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-07-07T10:56:01Z","title_canon_sha256":"1ad841489b202a1305434fefc2708f3ba4ed83fffcdcebabf97a64ec14bbbaac"},"schema_version":"1.0","source":{"id":"2107.03139","kind":"arxiv","version":1}},"canonical_sha256":"1343ad8beb1c48ea3b4e75b041b77d45a73d7e5ee639583eb2b1be69ac0584f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1343ad8beb1c48ea3b4e75b041b77d45a73d7e5ee639583eb2b1be69ac0584f8","first_computed_at":"2026-07-05T02:56:00.966935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:56:00.966935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sJwptKiBYyEsmkMmj4dE7S/hyb56fL3q+xsKNGmvsWp/MyrP5+KvTqIZFZHVWZ8cpYkPqAe/bY1j7OT8xMT7Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:56:00.967274Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.03139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19d633d5e64358ef7ee4261793a873d62a1a4d67bfc674daeecaba957d400655","sha256:376d22b626bc4e67eda86ddff163b83dca629e24f58fc43a4398d56b01212ef6"],"state_sha256":"8942f8156f3f9ab78a0314481a2e93d7b417c8c39432dbd588049854f0e8f4b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2t1VoBM05lXnNTFnOJ+ieswa/cAnF2D108MtEtVdlDtBd278cGvTq0QaUohJtW4bTiG9IWPAq2CuOVVzrNE3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:10:24.790523Z","bundle_sha256":"04ea8d88b20c43aaac35719a25ddbeabecdf1499d396b70331376601ca274421"}}